[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------[/tex]
[tex]\bf \textit{\underline{z} varies inversely with the product of \underline{x} and \underline{y}}\implies z=\cfrac{k}{xy}
\\\\\\
\textit{we also know that }
\begin{cases}
x=2\\
y=4\\
z=0.5
\end{cases}\implies 0.5=\cfrac{k}{(2)(4)}\implies 0.5=\cfrac{k}{8}
\\\\\\
4=k\qquad \qquad \boxed{z=\cfrac{4}{xy}}
\\\\\\
\textit{when x = 4 and y = 9, what is \underline{z}?}\qquad z=\cfrac{4}{(4)(9)}[/tex]
