Question

Write a direct variation equation that shows the relationship between x and y.

y = 15 when x = 6

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} y = 15\\ x = 6 \end{cases}\implies 15=k(6)\implies \cfrac{15}{6}=k\implies \cfrac{5}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = \cfrac{5}{2}x~\hfill`