In inverse variation, one variable is proportional to the reciprocal of the other.

y ∝ 1/x

We can change the "∝" sign of proportionallity to one that involves an equals sign by replacing the "∝"with "= k" where k is a constant to be found.

So y ∝ 1/x can be rewritten as y = k/x

**Example**

y varies inversely to x and y = 3 when x = 6.

Find y when x = 9.

**Answer**

y ∝ 1/x

y = k/x

Substituting y = 3 and x = 6, we get:

3 = k/6

k = 3 x 6 = 18

Thus y = 18/x is the formula that gives y in terms of x.

So when x = 9, we get** y **= 18÷9 **= 2**