[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" is directly proportional to "x"}}{y=kx}\qquad \textit{we also know that} \begin{cases} y = 35\\ x = 140 \end{cases} \\\\\\ 35=k140\implies \cfrac{35}{140}=k\implies \cfrac{1}{4}=k~\hfill \boxed{y=\cfrac{1}{4}x} \\\\\\ \textit{when x = 100, what is "y"?}\qquad y = \cfrac{1}{4}(100)\implies y = 25[/tex]
