Question

suppose y varies directly with x, and y = 8 when x = -6. what direct variation equation relates x and y? what is the value of y when x = -2?

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=8\\ x=-6 \end{cases}\implies 8=k(-6)\implies \cfrac{8}{-6}=k \\\\\\ -\cfrac{4}{3}=k\qquad therefore\qquad \boxed{y=-\cfrac{4}{3}x} \\\\\\ \textit{when x = -2, what is \underline{y}?}\qquad y=-\cfrac{4}{3}(-2)$