Question

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=4.5\\ x=3 \end{cases}\implies 4.5=\cfrac{k}{3}\implies 4.5(3)=k \\\\\\ 13.5=k\qquad therefore\qquad \boxed{y=\cfrac{13.5}{x}}$