video_title stringlengths 25 104 | Sentence stringlengths 91 1.69k |
|---|---|
Constructing, solving two-step inequality example Linear inequalities Algebra I Khan Academy.mp3 | Las Vegas, Mesa, and Denver. That has to be at least 120,000 people. Or another way of interpreting that is greater than or equal to 120,000. So to figure out how many people attended their show in Las Vegas, we just solve for L on this inequality. So if we simplify this left-hand side, we get the number of people in L... |
Constructing, solving two-step inequality example Linear inequalities Algebra I Khan Academy.mp3 | So to figure out how many people attended their show in Las Vegas, we just solve for L on this inequality. So if we simplify this left-hand side, we get the number of people in Las Vegas plus 45,000 plus 33,000. That is 78,000. It's going to be greater than or equal to 120,000. Now to isolate the L on the left-hand sid... |
Constructing, solving two-step inequality example Linear inequalities Algebra I Khan Academy.mp3 | It's going to be greater than or equal to 120,000. Now to isolate the L on the left-hand side of the inequality, we can subtract 78,000 from both sides. So minus 78,000. On the left-hand side, these cancel out. And we're just left with the number of people who attended the show in Las Vegas is going to be greater than ... |
Constructing, solving two-step inequality example Linear inequalities Algebra I Khan Academy.mp3 | On the left-hand side, these cancel out. And we're just left with the number of people who attended the show in Las Vegas is going to be greater than or equal to 120,000 minus 78,000. So 120,000 minus 80,000 is 40,000. That's going to be another 2,000. So the number of people who attended Las Vegas is going to be great... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So negative 5c is less than or equal to 15. I just rewrote it a little bit bigger. So if we want to solve for c, we just want to isolate this c right over here, maybe on the left-hand side. It's right now being multiplied by negative 5. So the best way to just have a c on the left-hand side is we can multiply both side... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | It's right now being multiplied by negative 5. So the best way to just have a c on the left-hand side is we can multiply both sides of this inequality by the inverse of negative 5, or by negative 1 5th. And let me just... So we want to multiply negative 1 5th times negative 5c, and we also want to multiply 15 times neg... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So we want to multiply negative 1 5th times negative 5c, and we also want to multiply 15 times negative 1 5th. I'm just multiplying both sides of the inequality by the inverse of negative 5, because this will cancel out with the negative 5 and leave me just with c. Now, I didn't draw the inequality here, because we hav... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | We are multiplying both sides by negative 1 5th, which is the equivalent of dividing both sides by negative 5. So we need to turn this from a less than or equal to a greater than or equal. And now we can proceed solving for c. So negative 1 5th times negative 5 is 1. So the left-hand side is just going to be c, is grea... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So the left-hand side is just going to be c, is greater than or equal to 15 times negative 1 5th. That's the same thing as 15 divided by negative 5. And so that is negative 3. So our solution is c is greater than or equal to negative 3. And let's graph it. So that is my number line. Let's say that is 0, negative 1, neg... |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So our solution is c is greater than or equal to negative 3. And let's graph it. So that is my number line. Let's say that is 0, negative 1, negative 2, negative 3. And I could go above 1, 2. And so c is greater than or equal to negative 3. So it can be equal to negative 3. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | Let's say that is 0, negative 1, negative 2, negative 3. And I could go above 1, 2. And so c is greater than or equal to negative 3. So it can be equal to negative 3. So I'll fill that in right over there. Let me do it in a different color. So I'll fill it in right over there. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So it can be equal to negative 3. So I'll fill that in right over there. Let me do it in a different color. So I'll fill it in right over there. And then it's greater than as well. So it's all of these values I am filling in in green. And you can verify that it works in the original inequality. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | So I'll fill it in right over there. And then it's greater than as well. So it's all of these values I am filling in in green. And you can verify that it works in the original inequality. Pick something that should work. Well, 0 should work. 0 is one of the numbers that we filled in. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | And you can verify that it works in the original inequality. Pick something that should work. Well, 0 should work. 0 is one of the numbers that we filled in. Negative 5 times 0 is 0, which is less than or equal to 15. It's less than 15. Now let's try a number that's outside of it. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | 0 is one of the numbers that we filled in. Negative 5 times 0 is 0, which is less than or equal to 15. It's less than 15. Now let's try a number that's outside of it. And I haven't drawn it here. I could continue with the number line in this direction. You would have a negative 4 here. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | Now let's try a number that's outside of it. And I haven't drawn it here. I could continue with the number line in this direction. You would have a negative 4 here. Negative 4 should not be included. And let's verify that negative 4 doesn't work. Negative 4 times negative 5 is positive 20. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | You would have a negative 4 here. Negative 4 should not be included. And let's verify that negative 4 doesn't work. Negative 4 times negative 5 is positive 20. And positive 20 is not less than 15. So it's good that we did not include negative 4. This is our solution, and this is that solution graphed. |
Multiplying and dividing with inequalities example Linear inequalities Algebra I Khan Academy.mp3 | Negative 4 times negative 5 is positive 20. And positive 20 is not less than 15. So it's good that we did not include negative 4. This is our solution, and this is that solution graphed. I wanted to do that in that other green color. Here you go. This is what it looks like. |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | So I'm assuming you have tried to do it on your own. And now let's see how we could actually tackle this. Now, one thing I want to point out, some of you might see these numbers all lined up and immediately want to say, hey, 7 plus 1 is 8, and 8 plus 3 is 11, carry the 1, et cetera, et cetera. And if you did that, you ... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | And if you did that, you would be making a mistake. Because you see right over here, these decimals aren't lined up. Here, if you did that, you would be adding the 7,000s to 100s. You would be adding 0 tenths to 5 ones. You would be adding 9 to 1 tenths, or essentially this is a 10 right over here. So the place is woul... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | You would be adding 0 tenths to 5 ones. You would be adding 9 to 1 tenths, or essentially this is a 10 right over here. So the place is would be all mixed up. So what you need to do is actually align the decimals so that your place values are aligned. So what you want to do is you want to align things up. So we could w... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | So what you need to do is actually align the decimals so that your place values are aligned. So what you want to do is you want to align things up. So we could write 9.087. And then we want to align the decimals. So let's align the decimal. This is what has to match up. And this is going to be 15.31. |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | And then we want to align the decimals. So let's align the decimal. This is what has to match up. And this is going to be 15.31. And this should hopefully make sense to you as well. This is 9 point something plus 15 point something. So it's going to be, if you add 9 to 15, you get it will be 24 point something, give or... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | And this is going to be 15.31. And this should hopefully make sense to you as well. This is 9 point something plus 15 point something. So it's going to be, if you add 9 to 15, you get it will be 24 point something, give or take a little bit. So when you see that here, here you have a 9 plus the 15. So you've lined up t... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | So it's going to be, if you add 9 to 15, you get it will be 24 point something, give or take a little bit. So when you see that here, here you have a 9 plus the 15. So you've lined up the appropriate place values. And now we are ready to add. It's a good idea to start with the smallest place value. So if you have any e... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | And now we are ready to add. It's a good idea to start with the smallest place value. So if you have any extra in a certain place, you can bring something into the next place value. So here you say 7 plus, well, this is 7 thousandths. It's in the thousandths place. And you might want to, you say, well, what do I add it... |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | So here you say 7 plus, well, this is 7 thousandths. It's in the thousandths place. And you might want to, you say, well, what do I add it to? There's no thousandths right over here. And you're right. There are no thousandths. So we could literally write 0 thousandths. |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | There's no thousandths right over here. And you're right. There are no thousandths. So we could literally write 0 thousandths. So 7 thousandths plus 0 thousandths is 7 thousandths. 8 hundredths plus 1 hundredth is 9 hundredth. 0 plus 0 tenths plus 3 tenths is 3 tenths. |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | So we could literally write 0 thousandths. So 7 thousandths plus 0 thousandths is 7 thousandths. 8 hundredths plus 1 hundredth is 9 hundredth. 0 plus 0 tenths plus 3 tenths is 3 tenths. We got our decimal. Then you have 9 ones plus 5 ones is 14 ones. Well, 14 ones is the same thing as 4 ones and 1 tenth. |
Adding decimals example 1 Decimals Pre-Algebra Khan Academy.mp3 | 0 plus 0 tenths plus 3 tenths is 3 tenths. We got our decimal. Then you have 9 ones plus 5 ones is 14 ones. Well, 14 ones is the same thing as 4 ones and 1 tenth. So we'll carry that 1 right over there. So this is just 1 tenth plus 4 ones is 14. And so then finally, you have 1 tenth plus another 10 is 2. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And just as a bit of review, that means equations of lines in the form of y is equal to mx plus b, where m is the slope and b is the y-intercept. So let's just do a bunch of these problems. So here they tell us that a line has a slope of negative 5, so m is equal to negative 5, and it has a y-intercept of 6. So b is eq... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So b is equal to 6, so this is pretty straightforward. The equation of this line is y is equal to negative 5x plus 6. That wasn't too bad. Let's do this next one over here. The line has a slope of negative 1 and contains the point 4 fifths comma 0. So they're telling us the slope, slope of negative 1. So we know that m... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Let's do this next one over here. The line has a slope of negative 1 and contains the point 4 fifths comma 0. So they're telling us the slope, slope of negative 1. So we know that m is equal to negative 1. But we're not 100% sure about where the y-intercept is just yet. So we know that this equation is going to be of t... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So we know that m is equal to negative 1. But we're not 100% sure about where the y-intercept is just yet. So we know that this equation is going to be of the form y is equal to the slope, negative 1x plus b, where b is the y-intercept. Now, we can use this coordinate information, the fact that it contains this point, ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Now, we can use this coordinate information, the fact that it contains this point, we can use that information to solve for b. The fact that the line contains this point means that the value x is equal to 4 fifths, y is equal to 0, must satisfy this equation. So let's substitute those in. y is equal to 0 when x is equa... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | y is equal to 0 when x is equal to 4 fifths, so 0 is equal to negative 1 times 4 fifths plus b. Let me scroll down a little bit. So let's see, we get 0 is equal to negative 4 fifths plus b. We can add 4 fifths to both sides of this equation. So we could add a 4 fifths there. We could add a 4 fifths to that side as well... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | We can add 4 fifths to both sides of this equation. So we could add a 4 fifths there. We could add a 4 fifths to that side as well. The whole reason I did that is so that cancels out with that, and you get b is equal to 4 fifths. So we now have the equation of the line. y is equal to negative 1 times x, which we write ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | The whole reason I did that is so that cancels out with that, and you get b is equal to 4 fifths. So we now have the equation of the line. y is equal to negative 1 times x, which we write as negative x, plus b, which is 4 fifths. Just like that. Now we have this one. The line contains the points 2, 6 and 5, 0. So they ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Just like that. Now we have this one. The line contains the points 2, 6 and 5, 0. So they haven't given us the slope or the y-intercept explicitly, but we can figure out both of them from these coordinates. The first thing we can do is figure out the slope. So we know that the slope m is equal to change in y over chang... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So they haven't given us the slope or the y-intercept explicitly, but we can figure out both of them from these coordinates. The first thing we can do is figure out the slope. So we know that the slope m is equal to change in y over change in x, which is equal to, what is the change in y? Let's start with this one righ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Let's start with this one right here. 6 minus 0. Let me do it this way. I want to make it color-coded. Minus 0. So 6 minus 0. That's our change in y. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | I want to make it color-coded. Minus 0. So 6 minus 0. That's our change in y. And our change in x is 2 minus 5. And the reason why I color-coded it is I wanted to show you, when I use this y term first, I use the 6 up here, that I have to use this x term first as well. So I wanted to show you, this is the coordinate 2,... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | That's our change in y. And our change in x is 2 minus 5. And the reason why I color-coded it is I wanted to show you, when I use this y term first, I use the 6 up here, that I have to use this x term first as well. So I wanted to show you, this is the coordinate 2, 6. This is the coordinate 5, 0. I couldn't have swapp... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So I wanted to show you, this is the coordinate 2, 6. This is the coordinate 5, 0. I couldn't have swapped the 2 and the 5, then I would have gotten the negative of the answer. But what do we get here? This is equal to 6 minus 0 is 6. 2 minus 5 is negative 3. So this becomes negative 6 over 3, which is the same thing a... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | But what do we get here? This is equal to 6 minus 0 is 6. 2 minus 5 is negative 3. So this becomes negative 6 over 3, which is the same thing as negative 2. So that's our slope. So, so far, we know that the line must be y is equal to the slope, we'll do that in orange, negative 2 times x plus our y-intercept. Now we ca... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So this becomes negative 6 over 3, which is the same thing as negative 2. So that's our slope. So, so far, we know that the line must be y is equal to the slope, we'll do that in orange, negative 2 times x plus our y-intercept. Now we can do exactly what we did in the last problem. We can use one of these points to sol... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Now we can do exactly what we did in the last problem. We can use one of these points to solve for b. We can use either one. Both of these are on the line, so both of these must satisfy this equation. I'll use the 5, 0 because it's always nice when you have a 0 there, the math is a little bit easier. So let's put the 5... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Both of these are on the line, so both of these must satisfy this equation. I'll use the 5, 0 because it's always nice when you have a 0 there, the math is a little bit easier. So let's put the 5, 0 there. So y is equal to 0 when x is equal to 5. So y is equal to 0 when you have negative 2 times 5, when x is equal to 5... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So y is equal to 0 when x is equal to 5. So y is equal to 0 when you have negative 2 times 5, when x is equal to 5, plus b. And so you get 0 is equal to negative 10 plus b. If you add 10 to both sides of this equation, let's add 10 to both sides, these two cancel out, and you get b is equal to 10 plus 0, or 10. So you ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | If you add 10 to both sides of this equation, let's add 10 to both sides, these two cancel out, and you get b is equal to 10 plus 0, or 10. So you get b is equal to 10. And now we know the equation for the line. The equation is y, let me do it in a new color, y is equal to negative 2x plus b, plus 10. And we are done. ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | The equation is y, let me do it in a new color, y is equal to negative 2x plus b, plus 10. And we are done. Let's do another one of these. Let's do another one of these. Alright, the line contains the points 3, 5 and negative 3, 0. Just like the last problem, we start by figuring out the slope. The slope, which we will... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Let's do another one of these. Alright, the line contains the points 3, 5 and negative 3, 0. Just like the last problem, we start by figuring out the slope. The slope, which we will call m, is the same thing as the rise over the run, which is the same thing as the change in y over the change in x. If you were doing thi... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | The slope, which we will call m, is the same thing as the rise over the run, which is the same thing as the change in y over the change in x. If you were doing this for your homework, you wouldn't have to write all this. I just want to make sure that you understand that these are all the same things. And then what is o... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And then what is our change in y over change in x? This is equal to, let's start with this side first, just to show you I could have picked either of these points. So let's say it's 0, 0, minus 5, minus 5, just like that. So I'm using this coordinate first. I'm kind of viewing it as the end point. 0, minus 5. And remem... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So I'm using this coordinate first. I'm kind of viewing it as the end point. 0, minus 5. And remember, when I first learned this, I would always be tempted to do the x in the numerator. No, you use the y's in the numerator. So that's the second of the coordinates. And then that is going to be over negative 3, negative ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And remember, when I first learned this, I would always be tempted to do the x in the numerator. No, you use the y's in the numerator. So that's the second of the coordinates. And then that is going to be over negative 3, negative 3, minus 3. This is the coordinate negative 3, 0. This is the coordinate 3, 5. We're subt... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And then that is going to be over negative 3, negative 3, minus 3. This is the coordinate negative 3, 0. This is the coordinate 3, 5. We're subtracting that. So what are we going to get? This is going to be equal to, I'll do it in a neutral color, this is going to be equal to, the numerator is negative 5, over negative... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | We're subtracting that. So what are we going to get? This is going to be equal to, I'll do it in a neutral color, this is going to be equal to, the numerator is negative 5, over negative 3, minus 3, is negative 6. So the negatives cancel out. You get 5 over 6. So we know that the equation is going to be of the form y i... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So the negatives cancel out. You get 5 over 6. So we know that the equation is going to be of the form y is equal to 5 6ths x, plus b. And now we can substitute one of these coordinates in to solve for b. So let's do, I always like to use the one that has a 0 in it. So y is 0 when x is negative 3, when x is negative 3,... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And now we can substitute one of these coordinates in to solve for b. So let's do, I always like to use the one that has a 0 in it. So y is 0 when x is negative 3, when x is negative 3, plus b. So all I did is I substituted negative 3 for x, 0 for y, and I know I can do that because this is on the line. This must satis... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So all I did is I substituted negative 3 for x, 0 for y, and I know I can do that because this is on the line. This must satisfy the equation of the line. And let's solve for b. So we get 0 is equal to, well if we divide negative 3 by 3, that becomes a 1. If you divide 6 by 3, that becomes a 2. So it becomes negative 5... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So we get 0 is equal to, well if we divide negative 3 by 3, that becomes a 1. If you divide 6 by 3, that becomes a 2. So it becomes negative 5, negative 5 halves, plus b. We can add 5 halves to both sides of the equation. Plus 5 halves, plus 5 halves. I like to change my notation just so you get familiar with both. And... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | We can add 5 halves to both sides of the equation. Plus 5 halves, plus 5 halves. I like to change my notation just so you get familiar with both. And so the equation becomes 5 halves is equal to, that's a 0, is equal to b. b is 5 halves. So the equation of our line is, y is equal to 5 6x, plus b, which we just figured ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And so the equation becomes 5 halves is equal to, that's a 0, is equal to b. b is 5 halves. So the equation of our line is, y is equal to 5 6x, plus b, which we just figured out is 5 halves. Plus 5 halves. And we are done. Let's do another one. We have a graph here. Let's figure out the equation of this graph. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And we are done. Let's do another one. We have a graph here. Let's figure out the equation of this graph. This is actually on some level a little bit easier. What's the slope? Slope is change in y over change in x. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Let's figure out the equation of this graph. This is actually on some level a little bit easier. What's the slope? Slope is change in y over change in x. Let's see what happens. When we move in x, when our change in x is 1, that is our change in x. So change in x is 1. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Slope is change in y over change in x. Let's see what happens. When we move in x, when our change in x is 1, that is our change in x. So change in x is 1. I'm just deciding to change my x by 1. Increment by 1. What is the change in y? |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So change in x is 1. I'm just deciding to change my x by 1. Increment by 1. What is the change in y? It looks like y changes exactly by 4. It looks like my delta y, my change in y, is equal to 4 when my delta x is equal to 1. So change in y over change in x. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | What is the change in y? It looks like y changes exactly by 4. It looks like my delta y, my change in y, is equal to 4 when my delta x is equal to 1. So change in y over change in x. Change in y is 4 when change in x is 1. So the slope is equal to 4. And now, what's its y-intercept? |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So change in y over change in x. Change in y is 4 when change in x is 1. So the slope is equal to 4. And now, what's its y-intercept? Here we can just look at the graph. It looks like it intersects the y-axis at y is equal to negative 6, or at the point 0, negative 6. So we know that b is equal to negative 6. b is equa... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And now, what's its y-intercept? Here we can just look at the graph. It looks like it intersects the y-axis at y is equal to negative 6, or at the point 0, negative 6. So we know that b is equal to negative 6. b is equal to negative 6. So we know the equation of the line. The equation of the line is y is equal to the s... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So we know that b is equal to negative 6. b is equal to negative 6. So we know the equation of the line. The equation of the line is y is equal to the slope times x plus the y-intercept. Actually, I should write that. Or minus 6. That is plus negative 6. So that is the equation of our line. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Actually, I should write that. Or minus 6. That is plus negative 6. So that is the equation of our line. Let's do one more of these. So they tell us that f of 1.5 is negative 3. f of negative 1 is 2. What is that? |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So that is the equation of our line. Let's do one more of these. So they tell us that f of 1.5 is negative 3. f of negative 1 is 2. What is that? All this is telling you, this is just a fancy way of telling you that the point when x is 1.5, when you put 1.5 into the function, the function evaluates as negative 3. So th... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | What is that? All this is telling you, this is just a fancy way of telling you that the point when x is 1.5, when you put 1.5 into the function, the function evaluates as negative 3. So this tells us that the coordinate 1.5, negative 3 is on the line. And then this tells us that the point when x is negative 1, f of x i... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | And then this tells us that the point when x is negative 1, f of x is equal to 2. This is just a fancy way of saying that both of these two points are on the line. Nothing unusual. I think the point of this problem is to get you familiar with function notation, for you to not get intimidated if you see something like t... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | I think the point of this problem is to get you familiar with function notation, for you to not get intimidated if you see something like this. If you evaluate the function at 1.5, you get negative 3. So that's the coordinate y. If you imagine that y is equal to f of x. So this would be the y coordinate, would be equal... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | If you imagine that y is equal to f of x. So this would be the y coordinate, would be equal to negative 3 when x is 1.5. Let's do this multiple times. Let's figure out the slope of this line. The slope, which is change in y over change in x, is equal to, let's start with 2 minus this guy, negative 3, right, these are t... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Let's figure out the slope of this line. The slope, which is change in y over change in x, is equal to, let's start with 2 minus this guy, negative 3, right, these are the y values, over negative 1 minus this guy. Let me write it this way. Negative 1 minus that guy. Minus 1.5. And I do the colors because I want to show... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | Negative 1 minus that guy. Minus 1.5. And I do the colors because I want to show you that the negative 1 and the 2 are both coming from this. That's why I used both of them first. If I used these guys first, I would have to use both the x and the y's first. If I use the 2 first, I have to use the negative 1 first. That... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | That's why I used both of them first. If I used these guys first, I would have to use both the x and the y's first. If I use the 2 first, I have to use the negative 1 first. That's why I'm color coding it. So this is going to be equal to 2 minus negative 3. That's the same thing as 2 plus 3. So that is 5. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | That's why I'm color coding it. So this is going to be equal to 2 minus negative 3. That's the same thing as 2 plus 3. So that is 5. 1 minus 1.5, or negative 1 minus 1.5 is negative 2.5. And 5 divided by 2.5 is equal to 2. So the slope of this line is negative 2. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So that is 5. 1 minus 1.5, or negative 1 minus 1.5 is negative 2.5. And 5 divided by 2.5 is equal to 2. So the slope of this line is negative 2. Actually, I'll take a little side to show you it doesn't matter what order I do this in, as long as I use, if I use this coordinate first, then I have to use that coordinate f... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So the slope of this line is negative 2. Actually, I'll take a little side to show you it doesn't matter what order I do this in, as long as I use, if I use this coordinate first, then I have to use that coordinate first. Let's do it the other way. If I did it as negative 3, negative 3 minus 2, minus 2, over 1.5 minus ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | If I did it as negative 3, negative 3 minus 2, minus 2, over 1.5 minus negative 1. This should be minus the 2, over 1.5 minus the negative 1. This should give me the same answer. This is equal to what? Negative 3 minus 2 is negative 5, over 1.5 minus negative 1. That's 1.5 plus 1. So it's over 2.5. |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | This is equal to what? Negative 3 minus 2 is negative 5, over 1.5 minus negative 1. That's 1.5 plus 1. So it's over 2.5. So once again, this is equal to negative 2. So I just want to show you, it doesn't matter which one you pick as the starting or the end point, as long as you do it, you're consistent. If this is the ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So it's over 2.5. So once again, this is equal to negative 2. So I just want to show you, it doesn't matter which one you pick as the starting or the end point, as long as you do it, you're consistent. If this is the starting y, this is the starting x. If this is the finishing y, this has to be the finishing x. But any... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | If this is the starting y, this is the starting x. If this is the finishing y, this has to be the finishing x. But anyway, we know that the slope is negative 2. So we know that the equation is y is equal to negative 2x, plus some y intercept. Let's use one of these coordinates. I'll use this one, since it doesn't have ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So we know that the equation is y is equal to negative 2x, plus some y intercept. Let's use one of these coordinates. I'll use this one, since it doesn't have a decimal in it. So we know that y is equal to 2. So y is equal to 2 when x is equal to negative 1. And of course, you have your plus b. So negative 2 times nega... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So we know that y is equal to 2. So y is equal to 2 when x is equal to negative 1. And of course, you have your plus b. So negative 2 times negative 1 is 2, plus b. So if you subtract 2 from both sides of this equation, minus 2, minus 2, we're subtracting it from both sides of this equation, you're going to get 0 on th... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So negative 2 times negative 1 is 2, plus b. So if you subtract 2 from both sides of this equation, minus 2, minus 2, we're subtracting it from both sides of this equation, you're going to get 0 on the left-hand side is equal to b. So b is 0. So the equation of our line is just y is equal to negative 2x. y is equal to ... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | So the equation of our line is just y is equal to negative 2x. y is equal to negative 2x. Or actually, if you wanted to write it in function notation, it would be that f of x is equal to negative 2x. I kind of just assumed that y is equal to f of x. But this is really the equation. They never mentioned y's here. So you... |
More examples of constructing linear equations in slope-intercept form Algebra I Khan Academy.mp3 | I kind of just assumed that y is equal to f of x. But this is really the equation. They never mentioned y's here. So you could just write f of x is equal to 2x right here. And each of these coordinates are the coordinates of x and f of x. So you could even view the definition of slope as change in f of x over change in... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | So what we really want to do is isolate the p on one side of this inequality, and preferably the left. That just makes it a little bit easier to read. It doesn't have to be, but we just want to isolate the p. So a good step to that is to get rid of this p on the right-hand side. And the best way I can think of doing th... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | And the best way I can think of doing that is subtracting p from the right. But of course, if we want to make sure that this inequality is always going to be true, if we do anything to the right, we also have to do that to the left. So we also have to subtract p from the left. And so the left-hand side, negative 3p min... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | And so the left-hand side, negative 3p minus p, that's negative 4p, and then we still have a minus 7 up here, is going to be less than p minus p. Those cancel out. It is less than 9. Now, the next thing I'm in the mood to do is get rid of this negative 7 or this minus 7 here so that we can better isolate the p on the l... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | So the best way I can think of to get rid of a negative 7 is to add 7 to it. Then it'll just cancel out to 0. So let's add 7 to both sides of this inequality. Negative 7 plus 7 cancel out. All we're left with is negative 4p. On the right-hand side, we have 9 plus 7 is 16. And it's still less than. |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | Negative 7 plus 7 cancel out. All we're left with is negative 4p. On the right-hand side, we have 9 plus 7 is 16. And it's still less than. Now, the last step to isolate the p is to get rid of this negative 4 coefficient. And the easiest way I can think of to get rid of this negative 4 coefficient is to divide both sid... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | And it's still less than. Now, the last step to isolate the p is to get rid of this negative 4 coefficient. And the easiest way I can think of to get rid of this negative 4 coefficient is to divide both sides by negative 4. So if we divide this side by negative 4, these guys are going to cancel out. We're just going to... |
Multi-step inequalities 3 Linear inequalities Algebra I Khan Academy.mp3 | So if we divide this side by negative 4, these guys are going to cancel out. We're just going to be left with p. We also have to do it to the right-hand side. Now, there's one thing that you really have to remember since this is an inequality. This is not an equation. If you're dealing with an inequality, and if you mu... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.