# If y varies inversely as x, how do you find the constant of variation if y = 5 when x = -1?

May 14, 2016

$y = \frac{- 5}{x}$

#### Explanation:

Let $k$ be a constant

Write as:$\text{ } y = \frac{k}{x}$

It is given that at y=5; x=-1

So by substitution

$\text{ "y=k/x" "->" } 5 = \frac{k}{- 1}$

Multiply both sides by $\left(- 1\right)$

$\text{ } \left(- 1\right) \times 5 = \frac{- 1}{- 1} \times k$

But $\text{ } \frac{- 1}{- 1} = + 1$

$\text{ } k = - 5$

So the equation is:

$\text{ } y = \frac{- 5}{x}$