Proportion

Proportion

If a "is proportional" to b (which is the same as 'a is in direct proportion with b') then as b increases, a increases. In fact, there is a constant number k with a = kb. We write a ∝ b if a is proportional to b.

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 ∝ 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

In this example we might then be asked to find the value of a when b = 2. Now that we have a formul ...