Identifying equations of proportional graphs
About this video
The video reads points from a graph, (0,0), (5,-2), (10,-4) and (-5,2), and checks whether the ratio y/x is the same for each. Since every ratio is -2/5 and the line passes through the origin, the relationship is proportional with equation y = -2/5 x.
You'll be able to
- read points from a graph and put them in a table.
- test whether a relationship is proportional by comparing y/x ratios.
- write the equation y = kx for a proportional graph.
Key words
- proportional relationship
- A relationship where y is always the same number times x, so y/x stays constant.
- constant of proportionality
- The number k in y = kx; here it is -2/5.
- origin
- The point (0,0) where the x- and y-axes cross.
- ratio
- A comparison of two numbers, like y to x, often written as a fraction.
Transcript
- [Instructor] So I have the graph of a relationship between X and Y. What I want you to do, and then we'll do this together, is see if we can write an equation that represents this relationship between X and Y. All right, let's do this together. And one way that we could do this is just think about some of the points that satisfy this relationship.
So for example, I will set up a little table right over here, X and then Y. And when we can see a few points that seem to be on this. It looks like we have the point (0,0). When X is zero, Y is zero. It looks like we have the point right over here when X is five, Y is negative two.
Let's see, we can maybe go, looks like over here, this is on the line as well. When X is 10, Y is negative four. We could also go in this direction. When X is negative five Y looks like it is two. So the first thing I like to test is, is this a proportional relationship?
And if it's a proportional relationship, that means that the ratio between X and Y when we're not at the origin is always going to be the same. We also know for a proportional relationship that we should go through the origin. We should go through the point (0,0).
So that one's looking good there. But if we look at the ratio of X over Y for all of those other points, what does it look like? Well, here it'd be five to negative two. Or actually let me do Y over X. I actually think that's a more interesting one. The ratio of Y to X, although it should still be the same in all cases.
This here is negative two fifths. Here it is negative four over 10, which is the same thing as negative two fifths. Here it is two over negative five, which is negative two fifths. So in every situation it looks like Y is negative two fifths times X Y is equal to negative two fifths times X.
We can verify that all of these points satisfy that. And this also looks like a proportional relationship from an equation point of view. In a proportional relationship, Y is equal to some constant times X. The constant of proportionality in this case is negative two-fifths.
We also see very clearly that we go through an origin. Another way to think about even the graph of an equation is you're looking at all of the XY pairs that satisfy this equation and then you are just plotting it. So even though I picked out the ones that are easy to spot, any of these points right over here will satisfy whatever the X and Y coordinates are.
That Y is negative two fifths times X.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.