Question

The pair of points is on the graph of an inverse variation. Find the missing value.

(2, 8) and (x, 3)

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{{\color{red}{ \textit{some value }}}}{\textit{something else}}\\ \quad \\
y&=\cfrac{{\color{red}{ n}}}{x}
&&\implies y=\cfrac{{\color{red}{ n}}}{x}
\end{array}
\\ \quad \\
{\color{red}{ n}}\to \textit{constant of variation}
\\ \quad \\
(2,8)\implies x=2\qquad y=8\qquad thus\implies y=\cfrac{{\color{red}{ n}}}{x}\to 8=\cfrac{{\color{red}{ n}}}{2}
\\ \quad \\
\textit{so, what's the constant of variation or }{\color{red}{ n}}?\)