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## 7th grade (Illustrative Mathematics)

### Unit 2: Lesson 8

Lesson 10: Introducing graphs of proportional relationships# Identifying proportional relationships from graphs

Worked example identifying proportional relationships from graphs.

## Video transcript

- [Narrator] 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. So, 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 two, Y is zero times X. While, when X is four, Y is one times X. And when X is six, Y looks
to be, 1 and 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 zero 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 points she gets. Plot the ordered 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
five targets hit, 15 points. So then I'm 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.