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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.
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 ...