Question

If y=1/2 when x=2, find y when x=3, given that y varies directly with x

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=(1)/(2)\\ x=2 \end{cases}\implies \cfrac{1}{2}=k2\implies \cfrac{1}{4}=k \\\\\\ \boxed{y=\cfrac{1}{4}x} \\\\\\ \textit{when x=3, what is \underline{y}?}\qquad y=\cfrac{1}{4}\cdot 3`