Question

Y is inversely proportional to x.

When y = 6, x = 8
a) Work out an equation connecting y and x.

Answer 1

`\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{y varies inversely with x}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{8}\implies 48=k\hspace{10em}\boxed{y=\cfrac{48}{x}}`