Question

(8,1) and (x,3) The pair of points is on the graph of an inverse variation. Find the missing value.

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf (\stackrel{x}{8},\stackrel{y}{1})\textit{ we know that } \begin{cases} x=8\\ y=1 \end{cases}\implies 1=\cfrac{k}{8}\implies 8=k \\\\\\ therefore\qquad \boxed{y=\cfrac{8}{x}} \\\\\\ (x,\stackrel{y}{3})\textit{ when y = 3, what is \underline{x}?}\qquad 3=\cfrac{8}{x}\implies x=\cfrac{8}{3}$