Direct Proportion
If two quantities
and
are in direct proportion then they increase together by the same ratio. If one doubles so does the other, and if one increases by a factor of 10, so does the other. We can write down the relationship between these two quantities in the form of an equation,
where 
is the constant of proportionality. We may have to find
but once we have found it, then we can findfor any given value of
orfor any given value of
Direct proportion is illustrated on the graph above. For this direct proportion relation
the gradient of the graph. We can also findif we are told specific values ofandIf we are told that
when
then
Now we know that
we can:
Findif
Findif
Inverse Proportion
Two quantitiesandare inversely proportional if their product is a constant
– we can also write this equation as
The graph of two quantities in inverse proportion is given below.
We can find k if we are told specific values ofandIf we are told that
when then
Now we know that
we can:
Findif
Findif