[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] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}\qquad \textit{we also know that} \begin{cases} x=\frac{2}{3}\\ y = 6 \end{cases}\implies 6=k\cfrac{2}{3} \\\\\\ 18=2k\implies \cfrac{18}{2}=k\implies 9=k~\hfill \boxed{y=9x} \\\\\\ when~x=10\frac{1}{3}\textit{ what is "y"?}\qquad y=9\left( 10\frac{1}{3} \right)\implies y=9\cdot \cfrac{31}{3}\implies y=93[/tex]
