# If y varies inversely as x, and y = 1 as x = -2, how do you find y for the x-value of -1?

Jun 16, 2016

$y = 2.$

#### Explanation:

Given that $y \propto \frac{1}{x} .$
$\therefore y = \frac{k}{x} ,$, or, $x y = k$ ...(1), where $k \ne 0$ is constant of variation.

To determine $k ,$ we use the given cond. that, $x = - 2 \Rightarrow y = 1.$

By (1) then, $k = - 2.$ Hence (1) $\Rightarrow x y = - 2.$...(2)

Now, when x=-1, y=?

(2) $\Rightarrow \left(- 1\right) y = - 2 ,$ or $y = 2.$

Jun 16, 2016

$y = 2$

#### Explanation:

This is an example of inverse proportion, or inverse variation.

To change a proportion into an equation, multiply by a constant and then use the values given to find the value of the constant.

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

$k = - 2 \times 1 = - 2$

So, $y = \frac{- 2}{x}$

When $x = - 1 , \text{ } y = \frac{- 2}{- 1}$