Question

Y varies directly as x. Y = 42 when x= 3 find y when x = 11

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}`

`\bf \textit{we also know that } \begin{cases} y = 42\\ x = 3 \end{cases}\implies 42=k(3)\implies \cfrac{42}{3}=k\implies 14=k \\\\\\ \textit{therefore}\qquad \qquad \boxed{y = 14x} \\\\\\ \textit{when x = 11 what is \underline{y}?}\qquad \qquad y = 14(11)\implies y = 154`