# If y=8, when x=4, how do you find x when y=2 given that y varies inversely as x?

Jan 23, 2017

## 16

#### Explanation:

$y$ varies inversely as $x$

$\implies y \text{ " alpha" } \frac{1}{x}$

$\implies y = \frac{k}{x}$

where $k$ is the constant of proportionality

to find $k$ we use the conditions given

$y = 8 , x = 4$

$8 = \frac{k}{4} \implies k = 32$

$\therefore y = \frac{32}{x}$

when $y = 2$

$2 = \frac{32}{x} \implies x = \frac{32}{2} = 16$