Question

Suppose that y varies inversely with x. Use the information to kind k, and then choose the equation of variation. x=2 when y=2

A k=4 ,y=4/x
B k=1 , y=1/x
C k=4 , y=4x
D k=1 , y=1x

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} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} x=2\\ y=2 \end{cases}\implies 2=\cfrac{k}{2}\implies 4=k~\hfill \boxed{y=\cfrac{4}{x}}`