Question

If y=-27 when x= -9 find x when y=42

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \textit{we know that } \begin{cases} y=-27\\ x=-9 \end{cases}\implies -27=k(-9)\implies \cfrac{-27}{-9}=k \\\\\\ 3=k\qquad therefore\qquad \boxed{y=3x} \\\\\\ \textit{when y = 42, what is \underline{x}?}\qquad 42=3x\implies \cfrac{42}{3}=x\implies 14=x$