Analyzing relationships between variables using tables and equations | 6th grade | Khan Academy

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. 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. We can see when the charging time is 15 minutes, the range is 180. So we can 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 km. So I could write that there.

Then we see when the charging time is 45 minutes, the range is 540 km. So that's all nice, but then they give us a few other points here. They say what happens when we are at T = 10 or T = 1, 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 * T, we know that when T equals 1, K is 12, and when T equals 10, 10 * 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 want to 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 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. 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.