Question

The value of y varies directly with x, and y = 12 when x = 16.

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=12\\ x=16 \end{cases}\implies 12=k16\implies \cfrac{12}{16}=k \\\\\\ \cfrac{3}{4}=k\qquad therefore\qquad \boxed{y=\cfrac{3}{4}x} \\\\\\ \textit{when x = 6, what is \underline{y}?}\qquad y=\cfrac{3}{4}(6)$