Question

Y varies directly as x and y = 18 when x= 1/2. write an equation that relates y and x

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=18\\ x=\frac{1}{2} \end{cases}\implies 18=k\cfrac{1}{2}\implies 18=\cfrac{k}{2} \\\\\\ 36=k\qquad therefore\qquad \boxed{y=36x}$