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we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so once again , that was pretty easy to figure out . this term goes away and you just have to say hey , nine times x is 72 , x would be eight . when y is equal to zero , x is eight .
what do `` x '' and `` y '' represent ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
is it just me , or does anyone else think that slope-intercept form is more standard that standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
how do you figure out what c is ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
and since i , at least i do n't like a decimal up here , let 's multiply the numerator and the denominator by two . you get negative nine over 16 . now once again , we had to do a little bit of work here .
can we have a negative exponent ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so when you go from eight to zero , your change in x is equal to negative eight . and to go from zero to 4.5 , your change in y is going to be 4.5 . so your slope , once you 've figured this out , you could say , `` okay , this is going to be `` change in y , 4.5 , over change in x , `` over negative 8 . '' and since i...
why is 8 becoming a negative ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so when you go from eight to zero , your change in x is equal to negative eight . and to go from zero to 4.5 , your change in y is going to be 4.5 . so your slope , once you 've figured this out , you could say , `` okay , this is going to be `` change in y , 4.5 , over change in x , `` over negative 8 . ''
why is n't 4.5 a negative ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
and you 'll be left with y is equal to negative 9/16x , that 's the slope , you see it right there , plus 72 over 16 , we already figured out that 's 9/2 or 4.5 . so i could write , oh i 'll just write that as 4.5 . and this form over here , much easier to figure out the slope and , actually , the y-intercept jumps out...
are there any more forms to write an equation in ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
to make a standard form equation , can i make a slope intercept form and move the mx to the y 's side ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
is n't it easy to figure out the slope in standard form by using the coefficients of the y and x terms ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
what does the c stand for ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
is it possible in the standard form to say m=b/a ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good...
is the slope of a line in standard form ( ax + by = c ) always equal to -a/b ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
what does c stand for ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how do you translate a graph into standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
the place where slope-intercept or point-slope form are frankly better is that it 's pretty easy to pick out the slope here , while in standard form you would have to do a little bit of work . you could use these two points , you could use the x and y-intercepts as two points and figure out the slope from there . so yo...
do you use the x and y intercepts ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
or , what i typically do if i 'm looking for the slope , i actually might put this into , into one of the other forms . especially slope-intercept form . but standard form by itself , great for figuring out both the x and y-intercepts and it 's frankly not that hard to convert it to slope-intercept form .
how do you write 3x-2=-16 in slope intercept form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
if we start with 9x plus 16y is equal to 72 and we want to put it in slope-intercept form , we can subtract 9x from both sides . you get 16y is equal to negative 9x , plus 72 . and then divide both sides by 16 .
why does sal use the equation 9x+16y=72 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
is there a difference between integers and real numbers ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so if nine times x is 72 , 72 divided by nine is eight . so x would be equal to eight . so once again , that was pretty easy to figure out .
how would you be able to solve the linear equation y= -3 when you do n't have an x ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
this is slope-intercept . slope- intercept . and these are just different ways of writing the same equations .
why and when does the slope exchange the demonitor with the numerator ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
if we start with 9x plus 16y is equal to 72 and we want to put it in slope-intercept form , we can subtract 9x from both sides . you get 16y is equal to negative 9x , plus 72 . and then divide both sides by 16 .
is 9x+16y=72 , the same as writing it like 9x+16y-72=0 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
this is slope-intercept . slope- intercept . and these are just different ways of writing the same equations .
why is m used to represent the slope ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how would you simplify an equation in standard form where everything is a fraction ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
could someone explain how to graph a standard form linear equation without changing it ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how do you write an equation in standard form with only 2 points ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
what 's the difference between real number and integers ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
another way is point-slope . point-slope form . and in point-slope form , if you know that some , if you know that there 's an equation where the line that represents the solutions of that equation has a slope m. slope is equal to m. and if you know that x equals , x equals a , y equals b , satisfies that equation , th...
how do you derive point-slope form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
this is slope-intercept . slope- intercept . and these are just different ways of writing the same equations .
if we already know what the slope is and what the y intercept is , then why not just plug the slope and y intercept into the slope intercept form and divide the y value out by 16 , rather than dividing each value out by 16 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
if we have the equation ax+by=c then -b shows the x intersect and -a shows the y intersect ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
in standard form can x end up being a fraction or a negative number ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how do you write an equation in standard form with integer numbers only with the m and b being fractions ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
another way is point-slope . point-slope form . and in point-slope form , if you know that some , if you know that there 's an equation where the line that represents the solutions of that equation has a slope m. slope is equal to m. and if you know that x equals , x equals a , y equals b , satisfies that equation , th...
you can go from slope point form to slope intercept but you ca n't go in reverse direction , right ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope .
wait so the a and b values are the slope , if you put them in the format of a/b ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how do we get c in the standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
and we 're left with 16y is equal to 72 . and so we could solve , we could solve that . so we could say , alright 16y is equal to 72 .
so to solve the problem , only x can be 0 while y is a number and vice-versa ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
now what about the y-intercept ? well , we said x equals zero , this disappears . and we 're left with 16y is equal to 72 .
y=2 4x+ 3y= 14 4x+ 3 x 2 = 14 would this still work instead of making x zero as well and going through the whole process again ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
in standard form ax+by=c is a should be posite or negative always ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
did mathematicians have no better reason to introduce standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
can a , b and c in the standard form be irrational numbers ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so if nine times x is 72 , 72 divided by nine is eight . so x would be equal to eight . so once again , that was pretty easy to figure out .
how would you find the x and y intercepts for 4x+y=0 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
and we 're left with 16y is equal to 72 . and so we could solve , we could solve that . so we could say , alright 16y is equal to 72 .
if i wanted to solve for y , would 4x be 0 , making y=0 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
would 6a + 6b = 12 be solved the same way as in standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
x is zero , y is one , two , three , 4.5 . and just with these two points , two points are enough to graph a line , we can now graph it . so let 's do that .
line p goes through the points [ -1,5 ] and [ 2,1 ] what is the y-intercept of line p ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
why a , b , c must be integers ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
what if my standard form equation is 2x - y = 17 what will my points be on my graph ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
let me . so when you go from eight to zero , your change in x is equal to negative eight . and to go from zero to 4.5 , your change in y is going to be 4.5 .
can `` x '' be negative ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers . and what i want to do in this video , like we 've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at ?
i know what the x and y are , but what does the a , b , c stand for ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope .
in what does he mean by m and b are constants ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
how do you get standard form from a graph ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
another way is point-slope . point-slope form . and in point-slope form , if you know that some , if you know that there 's an equation where the line that represents the solutions of that equation has a slope m. slope is equal to m. and if you know that x equals , x equals a , y equals b , satisfies that equation , th...
so what are the benefits of point-slope form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
is standard form the same as general form when converting linear equations into the slope and y-intercept ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
or , what i typically do if i 'm looking for the slope , i actually might put this into , into one of the other forms . especially slope-intercept form . but standard form by itself , great for figuring out both the x and y-intercepts and it 's frankly not that hard to convert it to slope-intercept form .
when converting standard form to slope intercept , what do you do if something is example 2y=3x+4 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so when y is zero , what is x ? so when y is zero , 16 times zero is zero , that term disappears , and you 're left with 9x is equal to 72 . so if nine times x is 72 , 72 divided by nine is eight .
9 why is y zero ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
this is slope-intercept . slope- intercept . and these are just different ways of writing the same equations .
am i crazy or did sal make a mistake by saying that the x intercept was -8 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
what does a , b , and c , in the linear standard form , mean ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants .
what does `` by '' mean ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope .
what does the `` b '' represent ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
would 18x-5y+0.2 be in standard form ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
standard . standard form . and standard form takes the shape of ax plus by is equal to c , where a , b , and c are integers .
in standard form , should a , b and c have a gcf of 1 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so once again , that was pretty easy to figure out . this term goes away and you just have to say hey , nine times x is 72 , x would be eight . when y is equal to zero , x is eight .
for example 10x+20y=100 should be written as x+2y=10 ?
we 've already looked at several ways of writing linear equations . you could write it in slope-intercept form , where it would be of the form of y is equal to mx plus b , where m and b are constants . m is the coefficient on this mx term right over here and m would represent the slope . and then from b you 're able t...
so if nine times x is 72 , 72 divided by nine is eight . so x would be equal to eight . so once again , that was pretty easy to figure out .
what would you use the x-intercept for ?
if you 've ever been around young children , you 're probably aware of the close bond that exists between mother and child , and scientists refer to this bond as attachment . but what causes this attachment ? why is there such a strong bond between mother and child ? for years , scientist thought that it had to do wit...
on the other hand , if you think that attachment is based on things like comfort , then you would assume that the monkey would spend most of it 's time around the cloth mother , because this is the mother that has the soft blanket , this is the mother that can provide contact comfort . well it turns out that the baby m...
does the cloth 'mother ' smell to the baby monkeys ?
if you 've ever been around young children , you 're probably aware of the close bond that exists between mother and child , and scientists refer to this bond as attachment . but what causes this attachment ? why is there such a strong bond between mother and child ? for years , scientist thought that it had to do wit...
and i should note now that even though we 're calling them mothers , we 're actually referring to two different vaguely monkey shaped structures that were placed in the cage with the baby monkey . the first alternative mother option was the wire mother . and this was a mother that had a vaguely face like shape on top o...
was the wire 'mother ' heated or cold ?
if you 've ever been around young children , you 're probably aware of the close bond that exists between mother and child , and scientists refer to this bond as attachment . but what causes this attachment ? why is there such a strong bond between mother and child ? for years , scientist thought that it had to do wit...
for years , scientist thought that it had to do with food . that a mom 's unique ability to feed her child is what resulted in attachment . but that seems a little cold and kind of discounts all the things that mothers provide for their children .
was there any attachment ( clinging ) whatsoever made between the infant monkey and the `` wire mom '' ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what is a real-life situation where someone would need to know the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
or is it impossible to reduce something under a square root sign ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
when graphing quadratic equations and also using the formula we look for x , would there be a formula for finding the y intercepts ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
how to find the quadratic equation when the roots are given ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of those numbers . so this actually does have solutions , but they involve imaginary numbers . so this actually has no real solutions , we 're tak...
how difficult is it when you start using imaginary numbers ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
does this simplification leave the square root of 39 alone ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
what does one do when b is a negative number ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
how would you put the quadratic equation be put into vertex form ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
also how could an equation in vertex form help you graph a quadratic equation ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we make this into a 10 , this will become an 11 , this is a 4 . it is 84 , so this is going to be equal to negative 6 plus or minus the square root of -- but not positive 84 , that 's if it 's 120 minus 36 . we have 36 minus 120 .
why can we not square the negative root thereby getting ( 36 +- 84 ) /36 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
what is the point in squaring the terms before find the square root ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is the quadratic formula generally learned in algebra 1 or 2 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 .
is the quadratic equation used to find the age of the universe , like 13.798 +/- 0.037 x 10^9 years , the +/- sign means there is two answers ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
and let 's just plug it in the formula , so what do we get ? we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared .
for example , the equation 20x^2+196x+288 i plugged the correct corresponding numbers into the quadratic formula and got two numbers but how would i put them into the ( x+a ) ( x+b ) groupings when the 20 is in front of the x ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
its vertex is sitting here above the x-axis and it 's upward-opening . it never intersects the x-axis . so at no point will this expression , will this function , equal 0 .
could we say then that the purpose of the quadratic equation is to find the intersections at the x-axis and that if it has `` no real solutions '' it simply means that the graph of the equation is somewhere above the x-axis ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
it 's worthless . it just gives me a square root of a negative number . it 's not giving me an answer .
in a quadratic formula , how would you factor a square root of a negative number ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
at 1 why does sal write the square root of 156 as the square root of 2 * 2 times the square root of 39 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of those numbers . so this actually does have solutions , but they involve imaginary numbers . so this actually has no real solutions , we 're tak...
how are real numbers different from complex numbers ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
so when you learn the quadratic formula knowing how to discover what x is by factoring becomes obsolete or it can be used for other purposes ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
when solving a quadratic using the quadratic formula is it acceptable to move move all the variables to the right side such as -9x^2=-x-4 or is it better to always move the variables to the left side ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 .
does the quadric formula work if the x is say x^4 or x^x^2 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there .
lets say the problem is x^2-225=0 would the quadratic formula still be able to work for a missing b value ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so let 's speak in very general terms and i 'll show you some examples . so let 's say i have an equation of the form ax squared plus bx plus c is equal to 0 . you should recognize this .
what is the surd form ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
if the b is already negative do you put it in the formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
let 's rewrite the formula again , just in case we have n't had it memorized yet . x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem .
when solving for x , why do you add -b plus or minus what has already been simplified and square rooted before diving by 2a ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
how do you get the quadratic formula from the original formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what is factoring , why do we use it , and how is it useful ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that with that -- since this is the first time we 're doing it , let me not skip too many steps .
why did sal write -4 for multiplying a and c ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so negative 21 , just so you can see how it fit in , and then all of that over 2a . a is 1 , so all of that over 2 . so what does this simplify , or hopefully it simplifies ?
will a always be 1 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 .
because a 1 is in front of the x ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
what is a integral root ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
its vertex is sitting here above the x-axis and it 's upward-opening . it never intersects the x-axis . so at no point will this expression , will this function , equal 0 .
in problems in which the quadratic formula solves as a solution which never intersects the x or y axis will the solution intersect the imaginary axes in the imaginary graph ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
i remember my 7th grade math teacher said `` five tomato '' to remember 5280 feet in a mile , so is there a trick like that which can be used on the quadratic equation ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
how do you do quadratic equations with one solution with quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . 2 square roots of 39 , i...
ca n't the b^2 inside the square root be simplified ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative will become positive . but it still does n't matter , right ? we could say minus or plus , that 's the same thing as plus or minus the square root of 39 nine over 3 .
4 why do you still have two answers does n't the + or - sign disappear after the sqr root is found ?