# How do you graph the line through (2,-9) perpendicular to x + 2y = 8?

Jun 27, 2017

See below.

#### Explanation:

We must first find the slope of the given line.

$x + 2 y = 8$

$2 y = 8 - x$

$y = 4 - \frac{1}{2} x$

So, the perpendicular line's slope is the opposite inverse of the given line, or $2$.

Since we are given that it passes through a point, we may use point-slope to write out the line.

Point-Slope: $y - {y}_{0} = m \left(x - {x}_{0}\right)$

Plugging in,

$y - \left(- 9\right) = 2 \left(x - 2\right)$

$y = 2 x - 4 - 9$

$y = 2 x - 13$

We can now graph this.

graph{2x-13 [-12.58, 27.42, -8.44, 11.56]}