Question

7. The value of x varies directly with y, and

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} x= \frac{1}{3}\\ y= 12 \end{cases}\implies 12=k\left( \cfrac{1}{3} \right)\implies 12=\cfrac{k}{3} \\\\\\ 36=k~\hspace{10em}\boxed{y=36x}$