# If Y varies inversely as x. If y=10 when x=4, how do you find y when x=2?

Jul 14, 2017

$y = 20$

#### Explanation:

If $y$ varies inversely as $x$, then $x y = k$, where $k$ is a constant.

$x y = k$
$10 \cdot 4 = k$
$40 = k$

To find $y$ when $x = 2$, substitute $2$ for $x$ and $40$ for $k$ in the equation.

$x y = k$
$2 \cdot y = 40$
$y = \frac{40}{2}$

$y = 20$