Question

Which equation is the direct variation equation if f(x) varies directly with x and f(x)=-18 when x=3

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{f(x)}{y}=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=-18\\ x=3 \end{cases}\implies -18=k3 \\\\\\ \cfrac{-18}{3}=k\implies -6=k\qquad therefore\qquad \boxed{\stackrel{f(x)}{y}=-6x}$