Question

Suppose y varies directly with x. If y=6 when x = -2,find x when y= 15

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=6\\ x=-2 \end{cases}\implies 6=k(-2)\implies \cfrac{6}{-2}=k \\\\\\ -3=k\qquad thus\qquad \boxed{y=-3x} \\\\\\ \textit{now, when y = 15, what is \underline{x}?}\qquad 15=-3x\implies \cfrac{15}{-3}=x`