Question

Please help me I got stuck here thank you!

Answer 1

`\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`

`\stackrel{\textit{y varies directly with x}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=(3)/(4)\\[1em] y=(1)/(3) \end{cases} \\\\\\ \cfrac{1}{3}=k\left( \cfrac{3}{4} \right)\implies \cfrac{(1)/(3)}{~~ ( 3)/(4 ) ~~}=k\implies \cfrac{1}{3}\cdot \cfrac{4}{3}=k\implies \cfrac{4}{9}=k ~\hfill \boxed{y=\cfrac{4}{9}x}`