# Inverse proportion word problems with graphs ( the meaning of y is inversely proportional to x)

If **y is inversely proportional
to x** then the formula connecting y and x is **y = k/x** (k divided by x). k is known as the constant of proportionality
which can be found by using the boundary conditions. The boundary conditions
are the values of x and y which are given in the question.

**Example 1**

If m is inversely proportional to n, and when n = 7 m = 8, find a formula for m.

Since m is inversely proportional to n then the formula is:

m = k/n.

All you need to do now is use the boundary conditions (n=7 and m=8) to calculate the value of the constant of proportionality. You find k, by subbing in these values into your formula:

8 = k/7.

Since k is being divided by 7, then all you need to do is multiply the 8 by 7:

8 × 7 = k

56 = k

You can now put this value of k back into the original formula:

m = 56/n

The graph of m and n is shown below. Notice that as n increases, m decreases. This is an example of inverse proportion.

**Example 2**

If p is inversely proportional to q², and when q = 4 p =2, find a formula for p.

Since p is inversely proportional to q² then the formula is:

p = k/q².

All you need to do now is use the boundary conditions (p=2 and q=4) to calculate the value of the constant of proportionality. So like example 1 sub these values into your formula:

2 = k/4².

You can now work out 4²:

2 = k/16

Since k is being divided by 16, then all you need to do is multiply the 2 by 16:

2 × 16 = k

32 = k

You can now put this value of k back into the original formula:

p = 32/q²

The graph of p and q is shown below. Notice again that as q increases, p decreases.

Now you have mastered inverse proportion, check out this next hub on direct proportion:

Direct proportion. How to write down a formula if y is directly proportional to x. Maths GCSE.

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## Comments 1 comment

Interesting, but a bit technical for most of us. I mean, "inversely proportional" basically means, the greater Y is, the lesser X is, correct? But that's not terribly clearly stated here, unless the reader already speaks math at least a little. If you're trying to reach folks who are struggling with math, you might want to do a little more explaining before diving into the formulae.