Question

Y is directly proportional to x,and y=216 when x=2. Find y when x=7.

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=216\\ x=2 \end{cases}\implies 216=k2\implies \cfrac{216}{2}=k \\\\\\ 108=k\qquad therefore\qquad \boxed{y=108x} \\\\\\ \textit{when x = 7, what is \underline{y}?}\qquad y=108(7)$