Proportion

If a ‘is proportional’ to b, we write a µ b .
a is proportional to b means that a = kb, where k is a constant (a fixed number), so as b increases, a increases.
The value of k will be the same for all values of a and b and so it can be found by substituting in values for 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 = ˝b

Similarly, if m is proportional to n˛, m = kn˛

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/a˛
when a = 3, b = 1
\ 1 = k/3˛
\ k = 9

Copyright © Matthew Pinkney 2003