Question

If the point (2, -10) lies on the graph of a direct variation, which represents the direct variation equation?

A: y = -20x B: y = -5x C: y = -20/x D: y = -5/x

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{2},\stackrel{y}{-10})~~ \textit{we know } \begin{cases} x=2\\ y=-10 \end{cases}\implies -10=k2\implies \cfrac{-10}{2}=k\implies -5=k \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-5x~\hfill`