# If y=9 when x=9, how do you find y when y=-27 given y varies inversely as x?

Jun 12, 2017

$x = - 3$ when $y = - 27$

#### Explanation:

Inversely: $y = \frac{k}{x} \text{ or using proportions: } {y}_{1} / {y}_{2} = {x}_{2} / {x}_{1}$

Using the two step method , find $k$ given $y \text{ and } x$:

$9 = \frac{k}{9}$

Multiply both sides by $9$ to eliminate the denominator on the right:

$9 \cdot 9 = \frac{k}{9} \cdot \frac{9}{1}$

$81 = k$

Now fill in the equation using $k$:

$\frac{- 27}{1} = \frac{81}{x}$

Find $x$ by using the cross product: $- 27 x = 81$

Divide both sides by $- 27 : \text{ } \frac{- 27 x}{-} 27 = \frac{81}{-} 27$

$x = - 3$

Using Proportions: ${y}_{1} / {y}_{2} = {x}_{2} / {x}_{1}$

$\frac{9}{-} 27 = \frac{x}{9}$

Use the cross product: $- 27 x = 81$

Divide both sides by $- 27 : \text{ } \frac{- 27 x}{-} 27 = \frac{81}{-} 27$

$x = - 3$