# How do you write the equation if P varies inversely as Q and Q = 2/3 when P = 1/2?

May 31, 2015

If P varies inversely as Q then
$\textcolor{w h i t e}{\text{XXXXX}}$$P \cdot Q = c$
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{w h i t e}{\text{XXXXX}}$ for some constant $c$

Given that $\left(P , Q\right) = \left(\frac{1}{2} , \frac{2}{3}\right)$ is a solution to this equation we have

$\textcolor{w h i t e}{\text{XXXXX}}$$\left(\frac{1}{2}\right) \cdot \left(\frac{2}{3}\right) = c$
$\textcolor{w h i t e}{\text{XXXXX}}$$\rightarrow c = 3$

So the required equation is
$\textcolor{w h i t e}{\text{XXXXX}}$$P \cdot Q = 3$