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## Operations and Algebraic Thinking 218-221

### Course: Operations and Algebraic Thinking 218-221 > Unit 5

Lesson 9: Analyzing relationships between variables# Analyzing relationships between variables

CCSS.Math:

Sal shows an example where, given a context and graph, we connect a table and equation to analyze the relationship between the variables in the context. Created by Sal Khan.

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## Video transcript

- [Narrator] We're told Rava
is researching an electric car. She finds this graph,
which shows how much range, measured in kilometers, the car gains based on charging time. All right, and they say, first, fill in the missing
values in the table below. And if you are so
inspired, pause this video, and see if you can have
a go at that as well. All right, well they give us a few points, and I'm assuming these
are points on a line. And we can see when the
charging time is 15 minutes, the range is 180. So we could see when the
charging time is 15 minutes, the range is 180. We can see when the
charging time is 30 minutes, the range is 360 kilometers,
so I could write that there. And then we see when the
charging time is 45 minutes, the range is 540 kilometers. So that's all nice. But then they give us a
few other points here. They say what happens when
we are at T equals 10, or T equals one, which
aren't easy to pick out here? But this is where it might be useful, if we assume that this is a line, what is the relationship between these? So let's see, to go from 15 to 180, it looks like you're multiplying by 12. To go from 30 to 360, it looks
like we're multiplying by 12. To go from 45 to 540, it looks like we are multiplying by 12. So assuming K is just
going to be 12 times T, we know that when T equals one, K is 12, and when T equals 10, 10 times 12 is 120. All right, now the second part,
they say write an equation Rava can use to find out
how much charging time, T, it takes to gain any number
of kilometers in range, K. All right, well we already
established a relationship. We said that K is equal
to 12 times whatever T is. That's what we just established
in this table up here, but that's not what they want. They wanna find out how
much charging time, T, it takes to gain any number
of kilometers in range, K. So what we need to do here is solve for T. So let's divide both sides by 12 to just have a T by itself
on the right-hand side. And we are going to be left
with T is equal to K over 12. T is equal to K over 12 and notice, you could put any number of
kilometers of range in here and you're essentially just
going to divide it by 12, and that will give you
how much charging time. And I guess this would assume
an infinitely large battery, which we know doesn't exist. But for the sake of this
problem, here we have it. Here is the equation Rava can use.