Question

Y varies directly as x. If y = -2 when x = 4, find x when y = 5.

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=-2\\ x=4 \end{cases}\implies -2=k4\implies \cfrac{-2}{4}=k \\\\\\ -\cfrac{1}{2}=k\qquad therefore\qquad \boxed{y=-\cfrac{1}{2}x} \\\\\\ \textit{now, if y = 5, what is \underline{x}?}\qquad 5=-\cfrac{1}{2}x`

Answer 2

x = -10 if im correct