Identifying proportional relationships from graphs | 7th grade | Khan Academy

We are asked how many proportional relationships are shown in the coordinate plane below, and we have the choices. But let's actually look at the coordinate plane below to think about how many proportional relationships are depicted here. So pause this video and try to answer that yourself.

So let's do this together. If we're thinking about a proportional relationship or the graph of a proportional relationship, there should be two things that we're looking for. One, it should be a line; it should be a linear relationship between the two variables. Y should be some constant, some proportionality constant times X.

So you immediately would rule out our green curve here because this is not a line. You don't have a constant relationship between Y being some proportionality constant times X. And for the same reason, you would rule out this blue curve.

Now what about this purple line? This might be tempting because it is a line, but it does not go through the origin. When X is 2, Y is 0 times X, while when X is 4, Y is 1 times X, and when X is 6, Y looks to be 1 1/3 times X. So you don't have the same proportionality constant the entire time. So we have zero proportional relationships depicted here, so I would pick 0 there.

Let's do one more example. Natalie is an expert archer. The following table shows her scores (points) based on the number of targets she hits. All right, targets hit and then the points she gets. Plot the order pairs from the table.

All right, so the first one is (1, 3). So here I'm doing it on Khan Academy. My horizontal axis is targets hit, and my vertical axis is points. So one target hit, three points. So this is going to be one target hit; this is going to be three points.

Then I have two targets hit, six points. So two targets hit, and I have six points. And then I'm gonna have three or five targets hit, 15 points. So then I'm going to have, going to have five targets hit, and that is going to be 15 points.

And so this is looking like a proportional relationship in every situation. My point is equal to three times the targets hit, so my proportionality constant is three. And you can see if you try to connect these dots with a line, it will be a line. A line can go through all three of these, and it will go through the origin.

So are Natalie's points proportional to the number of targets she hit? Yes, absolutely.