Question

Suppose y varies directly with x. If y = 6 when x = 2, find x when y = 12. 4 3

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} y=6\\ x=2 \end{cases}\implies 6=k(2)\implies \cfrac{6}{2}=k\implies 3=k \\\\\\ therefore\qquad \boxed{y=3x} \\\\\\ \textit{when y = 12, what is \underline{x}?}\qquad 12=3x\implies \cfrac{12}{3}=x\implies 4=x$