# How do you determine the constant of proportionality if P varies inversely as Q and Q=2/3 when P=1/2?

Sep 11, 2015

For the given constraints, the constant of proportionality is $\frac{1}{3}$

#### Explanation:

If $P$ and $Q$ vary inversely
$\textcolor{w h i t e}{\text{XXX")PQ=c color(white)("XXX}}$for some constant $c$ (the constant of proportionality)

We are told $Q = \textcolor{red}{\frac{2}{3}}$ when $P = \textcolor{b l u e}{\frac{1}{2}}$
So
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{\frac{1}{2}} \cdot \textcolor{red}{\frac{2}{3}} = c$

and
$\textcolor{w h i t e}{\text{XXX}} c = \frac{1}{3}$