# How do you find the inverse of y = (-1/2)x + 7?

Mar 28, 2017

${y}^{-} 1 = 2 x - 14$

#### Explanation:

To find the inverse of an equation, we switch $x$ and $y$:
$x = \left(- \frac{1}{2}\right) y + 7$

And solve for $y$:
$x \textcolor{w h i t e}{0000} = \left(- \frac{1}{2}\right) y + 7$
ul(color(white)(00)-7color(white)(=(-1/2))-7
$x - 7 = \left(- \frac{1}{2}\right) y$
ul(xx2color(white)(=()yyyy)xx2
$2 \left(x - 7\right) = y$

$y = 2 x - 14$

To write that this equation is the inverse of the original one, we write the expression as ${y}^{-} 1 = 2 x - 14$