Question

Y varies directly as x when x= 3 and y =12 find y when x =12

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} x=3\\ y=12 \end{cases}\implies 12=k3\implies \cfrac{12}{3}=k\implies 4=k \\\\\\ thus\qquad \boxed{y=4x} \\\\\\ \textit{when x = 12, what is \underline{y}?}\qquad \qquad y=4(12)$