Question

Suppose y varies directly with x. If y=-20 when x=2, find y when x=14

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=-20\\ x=2 \end{cases}\implies -20=k2\implies \cfrac{-20}{2}=k \\\\\\ -10=k\qquad therefore\qquad \boxed{y=-10x} \\\\\\ \textit{when x = 14, what is \underline{y}?}\qquad y=-10(14)$