# Question #0b00d

Apr 18, 2017

$y + 3 = - 2 \left(x + 1\right)$
$y = - 2 x - 5$

#### Explanation:

$x - 2 y = - 10$

Isolate $y$ to find slope intercept form:
$- 2 y = - x - 10$

$y = \frac{1}{2} x + 5$

Perpendicular lines have opposite reciprocal slopes, so the slope of the new perpendicular line would be $\frac{- 1}{\textcolor{red}{m}}$ where $\textcolor{red}{m}$ is the slope of the given line.

Original slope: $\frac{1}{2}$
Perpendicular slope: $- 2$

Equation of new line in point-slope form:
$y + 3 = - 2 \left(x + 1\right)$
$y = - 2 x - 2 - 3$
$y = - 2 x - 5$