# How do you write the equation of the line parallel to the line x + 4y = 6 and passes through (-8, 5)?

Apr 24, 2016

I found $x + 4 y = 12$

#### Explanation:

We can use the general relationship for the equation of a line passing through $\left({x}_{0} , {y}_{0}\right)$ and slope $m$ as:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
to be parallel the slope must be the same of your original line.
We write the original line (collecting $y$) as:
$y = - \frac{1}{4} x + \frac{6}{4}$
whose slope is $- \frac{1}{4}$
so we can find our parallel as:
$y - 5 = - \frac{1}{4} \left[x - \left(- 8\right)\right]$
$4 y - 20 = - x - 8$
so the equation will be:
$x + 4 y = 12$