[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"y" varies directly with }x^2}{y=kx^2}\qquad \textit{we also know } \begin{cases} y=8\\ x=2 \end{cases} \\\\\\ 8=k(2)^2\implies 8=4k\implies \cfrac{8}{4}=k\implies 2=k~\hfill \boxed{y=2x^2} \\\\\\ \textit{when x = 3, what is "y"?}\qquad y=2(3)^2\implies y=2(9)\implies y=18[/tex]
