Question

which equation is the direct variation equation if f(x) varies directly with x and f(x)=-9 when x = 3

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} \stackrel{f(x)}{y}=-9\\ x=3 \end{cases}\quad -9=k3\implies \cfrac{-9}{3}=k\implies \boxed{-3=k} \\\\\\ thus\qquad \qquad \stackrel{f(x)}{y}=-3x$