## Direct and Inverse Proportion

Direct Proportion

If two quantitiesandare 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 findbut once we have found it, then we can findfor any given value oforfor any given value of

Direct proportion is illustrated on the graph above. For this direct proportion relationthe gradient of the graph. We can also findif we are told specific values ofandIf we are told thatwhenthen

Now we know thatwe can:

Findif

Findif

Inverse Proportion

Two quantitiesandare inversely proportional if their product is a constant– we can also write this equation asThe graph of two quantities in inverse proportion is given below.

We can find k if we are told specific values ofandIf we are told thatwhen then

Now we know thatwe can:

Findif

Findif