# How do you write an inverse variation equation given y=-1 when x=-12?

Dec 23, 2016

$\textcolor{g r e e n}{x \cdot y = 12}$

#### Explanation:

If $x$ and $y$ form an inverse variation then
$\textcolor{w h i t e}{\text{XXX}} x \cdot y = k$ for some constant $k$

Given that $\left(x = - 12 , y = - 1\right)$ is a solution to the required relation:
$\textcolor{w h i t e}{\text{XXX}} \left(- 12\right) \cdot \left(- 1\right) = k$

$\Rightarrow k = 12$

Dec 23, 2016

$y = \frac{12}{x}$

#### Explanation:

In an inverse variation - or inverse proportion, as one quantity increases the other decreases.

This can be written as: $y \propto \frac{1}{x}$

Variations (proportions) are linked by a constant (k)

We can write a variation as an equation by using the constant.

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

$x \times y = k \text{ } \leftarrow$now we can find a value for $k$ using the values of $x \mathmr{and} y$ which were given

$k = - 12 \times - 1 = 12$

The equation is therefore: $y = \frac{12}{x}$

This is the equation for a hyperbola which is the graph of inverse proportion.