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

Feb 22, 2016

The only purpose of giving the parallel line is to find the slope of the new equation. (parallel lines have the same slope)

So, first we find the slope of the given line

$x + 4 y = 6$

$4 y = - x + 6$

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

Okay, the slope of this line is -1/4, so the slope of the new line is also -1/4 because it is parallel

Now for the new line, we have $y = - \frac{1}{4} x + b$

Since we are given a point, we can just plug in -8 for x and 5 for y and solve for the missing variable b.

$5 = - \frac{1}{4} \left(- 8\right) + b$

$5 = 2 + b$

$3 = b$

So we have all of our missing pieces, and we put it into one equation.

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

And we are done.