[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{4} \implies 24=k~\hfill \boxed{y=\cfrac{24}{x}} \\\\\\ \textit{when x = 0.5, what is "y"?}\qquad y=\cfrac{24}{0.5}\implies y=48[/tex]
