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NationalTutoringObservatory
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MathEd-PII

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volunteer
Okay, so in general here, what they are asking you to do is to "solve each system" of equations by graphing.
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volunteer
What that means is that they are giving you the equation of two different lines and asking you "where do these lines cross"?
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volunteer
So what we'll do is to graph each line (as best we can) and then look to see where they intersect.
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volunteer
Okay so far?
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student
Yes
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volunteer
In graphing the line, the easiest way to do it is to just plot two points and then connect the dots.
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volunteer
Or, you can convert each equation into a y = mx + b format like you've done here.
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volunteer
Then you can easily plot the y intercept at b, and then move up/down m units in slope to create your second point. Then connect the dots.
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student
Yes so i just went through the whole process of question #33 with another Tutor Provider tutor and i think i did fairly well but now here the y intercept is a fraction so is that incorrect
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volunteer
That's correct - the slope can be any number, including fractions.
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volunteer
So how did you find the point (-3, -4) in the previous problem?
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volunteer
I don't see any graphing...
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volunteer
Brooklyn !!!
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[ { "pii_type": "LOCATION", "surrogate": "Brooklyn", "start": 0, "end": 8 } ]
volunteer
I saw that.
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volunteer
So, if it were me, I'd not bother changing the format into the y = mx + b format.
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volunteer
Just get two points for each line and graph them. Boom done.
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student
Huh
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volunteer
So let's graph the first line - see what I'm writing?
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student
Yes
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volunteer
And we only need 2 points to draw the line, right?
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student
Right
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volunteer
So let's make it easy on ourselves and find the points by first setting x = 0 and solve for y
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volunteer
Then we set y = 0 and solve for x.
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volunteer
Okay?
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student
Okay..
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volunteer
So if we set x = 0, we get y = 12/-8
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volunteer
or -1.5
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volunteer
And if we set y = 0, we get x = 12/-3 or -4
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volunteer
Okay so far?
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student
Ive never seen anyone do this method
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volunteer
It's the easiest way to do these (by graphing).
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volunteer
When you solve them NOT by graphing, you'd solve each equation for y (or x, doesn't matter), then set them equal and solve for the other variable.
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volunteer
But that's now that we're being asked to do here..
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volunteer
Can you plot those two points on your graph paper (since your graphs are clean and neat and mine aren't) ???
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student
Ok
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volunteer
So here when x = 0, y = -48/32 = -1.5
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volunteer
And when y = 0, we get x = -4
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volunteer
Hmm - notice anything?
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student
They’re the same
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volunteer
:-)
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volunteer
Yup.
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volunteer
In general, as you got thru these type of problems, you'll get one of 3 different outcomes.
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volunteer
1. The lines will touch once, giving you one ordered pair (simple answer).
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volunteer
2. The lines are parallel but have different y intercepts. Hence they NEVER touch (no answers).
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volunteer
3. The lines are parallel and line "on top of each other" which is the case here.
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volunteer
But backing up, does this "plot two points for each line and connect the dots" idea make sense?
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student
No i am confused on how you came up with these coordinates
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volunteer
What I did (for each line) was to create two points.
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volunteer
In theory, you can plug any number in for x (like 27) and see what y value that gives you.
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volunteer
But, because I'm lazy and like to work with easy numbers, I chose x = 0 and solved for y.
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volunteer
But in general, you can plug in ANY number you want. You're just finding one of the two points that you need.
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student
Okay
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volunteer
Again, this is just a visual way to "solve the solution".
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volunteer
Wanna do another, or are you good with this technique?
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volunteer
Or, you can stay with your "solve them algebraically" method and graph once done...
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student
So the answer for the question is no answer because theyre on top of eachother?
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volunteer
The answer (depends on the vocabulary of your text) would be that there are infinite solutions to the problem set.
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volunteer
There's not just one point where the lines intersect, ALL the points are intersecting.
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student
Okay
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volunteer
Another thing I wanted to mention is that sometimes they won't give you the equations for the lines
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volunteer
They'll just give you a few points for each line and ask "where do these lines touch?"
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volunteer
That's why this "connect the dots" thingy is important.
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student
Im sorry Mr. David but i like y = mx + b better because i can visualize everything and i feel like you just did some magic i dont understand your way
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[ { "pii_type": "PERSON", "surrogate": "Mr. David", "start": 9, "end": 18 } ]
volunteer
Yep, I get it.
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volunteer
So do you wanna do another one, or are you all set for now?
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student
Let’s do the next one
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student
It’s #39
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volunteer
36?
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student
My teacher assigns problems randomly
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volunteer
Chicago !
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[ { "pii_type": "LOCATION", "surrogate": "Chicago", "start": 0, "end": 7 } ]
volunteer
This is a vocabulary question, so to say.
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volunteer
What do those phrases mean?
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student
Omg
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student
I dont even know
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student
😣
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volunteer
Better ask Mr. Mr. Harrison.
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[ { "pii_type": "PERSON", "surrogate": "Mr. Harrison", "start": 15, "end": 27 } ]
volunteer
It's those same 3 cases I mentioned a while ago methinks.
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volunteer
hi! how are you doing
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student
good and you
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volunteer
great!
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volunteer
what do you need help with today
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student
i need help with parallel and perpendicular lines
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volunteer
got it
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volunteer
do you have a specific question
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volunteer
that you want to work through?
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student
yes i shared my screen so you're able to see the problem
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volunteer
yes
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volunteer
do you know where to start
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student
i found the sqaure roots by doing a^2+b^2=c^2
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student
and then i added them and got 6square root of five
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student
i can show you my steps on the white board
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volunteer
which part are we talking about?
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student
I finished my work and i got to that point and don't know what else to do
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volunteer
ok i see your work
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volunteer
you got those numbers from solving part a and b right
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student
I got these numbers by drawing a graph and seeing the distance between each triangle
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volunteer
you got 6square root of 5 for the total distance from A-X-Y-B
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student
yes
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volunteer
the question wants to know if that is longer or shorter than just going from A-B
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student
how would i do that
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