Two variables and are proportional if the ratio between them is constant. That means you always get the same answer when you divide by , regardless of where you are along the two graphs.
Two variables, and , are proportional if
where is a constant.
Saying that is the same as saying that :
Proportional functions are actually just a special case of linear functions, . What has happened is that , so is gone. This means that the graph intersects the -axis at the origin each time. In addition, the slope is replaced by the proportionality constant . Here are a few examples:
This graph shows , that is, . Since the graph is proportional, for all the coordinates on the graph, if you divide the -coordinate by the -coordinate, the answer is .
Is the graph proportional?
You can find that out by doing a few conversions:
You have determined that or , so the graph is proportional.
You have been given the following points:
-values 1 2 3 4 5 -values 7 14 21 28 35
Are these points part of a proportional function?
From the theory, you know that if you divide the -value by the -value, and the answer is the same each time, all points belong to a proportional function. You check the points from the table:
Because all the answers are the same, you are working with a proportional function. The function is .