# How do you write the inverse variation equation of the following. Y varies inversely with x and y = -12 when x = 6?

Jul 3, 2016

Inverse variation equation is $y = - \frac{72}{x}$

#### Explanation:

When $y$ varies inversely with $x$, we have $y \propto \frac{1}{x}$ i.e.

$y = \frac{1}{x} \times k$, where $k$ is a constant. In other words, multiplying both sides by $x$, we get

$x \times y = k$

Here $y = - 12$, when $x = 6$

i.e. $6 \times \left(- 12\right) = k$ or $k = - 72$

Hence inverse variation equation is $y = - \frac{72}{x}$