# Assume y varies inversely as x, how do you write the equation given y=-6 when x=-3?

May 29, 2017

$y \propto \left(\frac{1}{x}\right)$

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

With x = -3 and y = -6 we have:

$- 6 = \frac{k}{-} 3$

=> k = 18

Then, $y = \frac{18}{x}$

or, $x y = 18$

:)>

May 29, 2017

$y = \frac{18}{x}$

#### Explanation:

This sounds like inverse proportionality.

The standard writing for such a formula is: $y = \frac{k}{x}$

Given the information, y = -6 when x =-3, we can find the constant "k".
$- 6 = \frac{k}{-} 3 \iff k = - 6 \cdot \left(- 3\right) = 18$

Now we know "k", we write the formula that sitifies y = -6 when x = -3 as $y = \frac{18}{x}$