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Inversely Proportional Functions


Two variables x and y are inversely proportional if their product is constant. That means you always get the same answer when you multiply x and y together.

Theory

Inverse Proportionality

Two variables x and y are inversely proportional if

y = k x

where k is a constant.

Example 1

Saying that y = k x is the same as saying that x y = k: x y = k, x0 x y x = k x, x0 y = k x, x0

Example 2

This graph shows y = 1 x, that is, k = 1. The graph is inversely proportional, so for all points on the graph, if you multiply the x-coordinate by the y-coordinate, the answer is k = 1.

The graph of y=1/x

Example 3

Is the graph y = 2 3x inversely proportional?

You can find that out by doing a few conversions: y = 2 3x = 2 1 3 x = 2 3 1 x 0.67 1 x 0.67 x

You’ve found that k = 2 3 0.67, so the graph is inversely proportional.

Example 4

You have been given the following points:







x-values 1 2 3 4 5






y -values 20 10 7 5 4






Do the points follow an inversely proportional function?

From the theory, you know that if multiply the x-value by the y-value and the answer is the same for all points, then the points follow an inversely proportional function. You check the points from the table: 1 20 = 20 2 10 = 20 3 7 = 21 4 5 = 20 5 4 = 20

Because one of the answers is not the same as the others, they do not follow an inversely proportional function.

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