If a ‘is proportional’ to b, we write a µ
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.
If a µ b, and b = 10
when a = 5, find an equation connecting a and b.
a = kb (1)
the values of 5 and 10 into the equation to find k:
5 = 10k
so k =
substitute this into (1)
a = ˝b
Similarly, if m is proportional to n˛, m = kn˛
If a and b are inversely proportionally to one another,
\ a = k/b
In these examples, k is
known as the constant of variation.
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 = k/3˛
\ k = 9
Copyright © Matthew Pinkney 2003