Direct proportions are direct multiplicative links between two values e.g. there is a direct proportion between centimetres (cm) and metres (m). We know that 100cm=1m, so the multiplier is always . So as one quantity increases, the other quantity increases at the same rate.
If is directly proportional to , we write and this is equal to , for some constant k. The constant can be calculated from the information provided about x and .
The symbol for direct proportion is:
If is directly proportionate to p then this means that , where is a natural number showing that is a multiple of .
There are 4 steps to follow when dealing with direct proportion:
Suppose y varies directly as and that y=12 when .
Form an equation connecting x and y, then use it to find the value of y when x=5. Also, find the value of x when y=108
The value of is directly proportional to . When , . We know that , therefore . As a result, . The final equation gives .