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

1 answer:

3 0

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

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

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