**Proportion**

If a is proportional to b,

a µ b

and a = kb, where k is a constant

The value of k will be the same for all values of a and b.

*Example*:

If a µ b, and b = 10 when a = 5, find an equation connecting a and b.

a = kb (1)

Substitute the values of 5 and 10 into the equation to find k:

5 = 10k

so k = 1/2

substitute this into (1)

__a = ½b__

__ __

Similarly, if m is proportional to n², m = kn²

**Inverse Proportion**

If a and b are inversely proportionally to one another,

a µ1/b

\ a = k/b

In these examples, k is known as the constant of variation.

*Example*:

If b is inversely proportional to the square of a, and when a = 3, b = 1, find the constant of variation.

b = k/a²

when a = 3, b = 1

\ 1 = k/3²

\ __k = 9__