Question

If '$x$' varies inversely as '$y$' and $x=7$ when $y=9$:
(a) Find constant of variation $\left(k\right)$.
(b) Write equation of variation.
(c) Find '$y$' when $x=9$.

Answer 1

(a) $x\propto \frac{1}{y}$
$\Rightarrow$ $x=\frac{k}{y}$
$\Rightarrow$ $7=\frac{k}{9}$
$\Rightarrow$ $k=7\times 9$
$\therefore$ $x=63$
$x=\frac{63}{y}$
$\Rightarrow$ $y=\frac{63}{x}$
$\Rightarrow$ $y=\frac{63}{9}$
$\therefore$ $y=7$