# Suppose y varies inversely with x. How do you write an equation for the inverse variation for Y = 5 when x = -5?

Mar 26, 2016

$\text{ } y = \frac{- 25}{x}$

#### Explanation:

As $x$ increases the $y$ decreases.

$\implies y \to \frac{1}{x} \text{ }$

$\frac{1}{x}$ becomes smaller as $x$ becomes bigger.

To complete this picture we need a constant

Let the constant be $k$

Then

$y \text{ "=" "kxx1/x" " =" } \frac{k}{x}$

We are told that when $y = 5 \text{ ; } x = - 5$

So we have

$y = \frac{k}{x} \text{ " ->" } 5 = \frac{k}{- 5}$

So $k = \left(+ 5\right) \times \left(- 5\right) = - 25$

Thus the equation becomes:$\text{ } y = \frac{- 25}{x}$