Question

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

Answer 1

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

(b) $x=\frac{63}{y}$

(c) $y=\frac{63}{x}$
$\Rightarrow y=\frac{63}{9}$
$\therefore y=7$.