Question

Write the equation of the line in slope-intercept form that is parallel to y=1/4x-4 and passes through (-8,2).

Answer 1

Parallel lines have equal slopes.

The slope of the line given is 1/4

So the line parallel will also have slope of 1/4.

The slope intercept form is:

$y=mx+b$

Since we know the slope, we can write:

$y=\frac{1}{4}x+b$

It passes through (-8,2). So we plug into x and y and find b:

$\begin{gathered} y=\frac{1}{4}x+b \\ 2=\frac{1}{4}(-8)+b \\ 2=-2+b \\ b=2+2 \\ b=4 \end{gathered}$

So, the equation of the lline parallel would be:

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