In maths, we say that two quantities are proportional if as one of them changes, the other one also changes in a specific way. There are two types of proportionality that you need to be familiar with.
If two quantities, A and B, are directly proportional, then as one increases the other also increases at the same rate, e.g. as one doubles, the other one also doubles. To express this, we use the proportionality symbol, \propto, and write
A \propto B,
which reads like “A is directly proportional to B”. However, there isn’t much we can do with A \propto B as it is, so we turn it into the equation
A = kB,
where k is the number which tells us how A and B are related. It is called the constant of proportionality. When you know the value of this constant, you can put it to good use. Let’s see an example.
Example: y is directly proportional to x. When y = 24, x = 8. Work out the value of y when x = 2.
We have that y is directly proportional to x, i.e. y \propto x. Then, expressing this as an equation we get
y = kx
In the question we’re given that when y = 24, x = 8. Substituting these into the equation above, we get 24 = 8 \times k, and so k = 24 \div 8 = 3. Thus, the proportionality equation becomes
y = 3x
We can now use this to work out that when x = 2, y = 3 \times 2 = 6. If you are a foundation student, you won’t explicitly be asked to form an equation like y = 3x. However, you will be expected to know how to work with constants of proportionality and use such an equation, so all of this content is still important to you.