Answer
$y=\frac{1}{4}x+3$
Work Step by Step
The given point is $(-4,2)$.
The given equation of the line is
$\Rightarrow y=\frac{1}{4}x+1$
Slope of the line is $m=\frac{1}{4}$.
Slope of the parallel line is $m=\frac{1}{4}$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $\frac{1}{4}$ for $m,-4$ for $x,$ and $2$ for $y$.
$\Rightarrow 2=\frac{1}{4}(-4)+b$
Simplify.
$\Rightarrow 2=-1+b$
Add $1$ to each side.
$\Rightarrow 2+1=-1+b+1$
Simplify.
$\Rightarrow 3=b$.
The equation of the parallel line is
$\Rightarrow y=\frac{1}{4}x+3$.
