# How do you write an equation of a line passing through (-8, -5), perpendicular to x + 4y = 6?

Jul 13, 2017

I got: $4 x - y = - 27$

#### Explanation:

We can write our line in the slope-intercept form $y = m x + c$ so that we can "see" the slope $m$:

$y = - \frac{1}{4} x + \frac{6}{4}$

$y = - \frac{1}{4} x + \frac{3}{2}$

so that the slope will be $m = - \frac{1}{4}$

The perpendicular to this line will have a slope:

$m ' = - \frac{1}{m} = 4$

we then use the general form for a line through a point of coordinates $\left({x}_{0} , {y}_{0}\right)$ and slope $m '$ as:

$y - {y}_{0} = m ' \left(x - {x}_{0}\right)$

or:

$y - \left(- 5\right) = 4 \left(x - \left(- 8\right)\right)$

$y = 4 x + 32 - 5$

$y = 4 x + 27$

or

$4 x - y = - 27$