# What is the equation of the line which is perpendicular to 2x+y=-4 which passes through the point (2,-8)?

Nov 17, 2017

$y = \frac{1}{2} x - 9$

#### Explanation:

Given equation : $2 x + y = - 4$

We rewrite this in Slope-Intercept form, that is;

$y = - 2 x - 4$

The slope in this equation's case is $m = - 2$

Therefore, the slope of a line that is perpendicular to this line is going to be the negative reciprocal of the given slope.

$m = - \left(- \frac{1}{2}\right) = \frac{1}{2}$

The y-intercept can be determined from the coordinates provided.
$\left(2 , - 8\right) .$

Substitute the values of the x and y coordinate in its Slope-Intercept form to determine the $y$-intercept:

$y = m x + b$
$- 8 = \left(\frac{1}{2}\right) \left(2\right) + b$
$b = - 9$

Therefore, the equation of the line is $y = \frac{1}{2} x - 9$