Identifying proportional relationships from graphs
About this video
The video shows how to spot a proportional relationship on a graph: it must be a straight line through the origin. It rules out two curves and a line that misses the origin, then plots an archer's points (1, 3), (2, 6) and (5, 15), which lie on a line through the origin with constant 3.
You'll be able to
- identify a proportional relationship on a graph as a line through the origin.
- explain why a curve or a line that misses the origin is not proportional.
- plot points from a table and find the proportionality constant.
Key words
- origin
- The point (0, 0) where the x-axis and y-axis meet.
- linear
- Forming a straight line.
- proportionality constant
- The number k in y = kx that stays the same for every point.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.