Answer
The value of slope is wrong.
The correct equation of the line is
$y=\frac{1}{4}x+\frac{11}{4}$
Work Step by Step
The given point is $(x_1,y_1)=(1,3)$.
The given equation of the line is
$\Rightarrow y=\frac{1}{4}x+2$
Slope of the line is $m=\frac{1}{4}$.
Slope of the parallel line is $m=\frac{1}{4}$.
The point-slope form is
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $\frac{1}{4}$ for $m,1$ for $x_1,$ and $3$ for $y_1$.
$\Rightarrow y-3=\frac{1}{4}(x-1)$
Use distributive property.
$\Rightarrow y-3=\frac{1}{4}x-\frac{1}{4}$
Add $3$ to each side.
$\Rightarrow y-3+3=\frac{1}{4}x-\frac{1}{4}+3$
Simplify.
$\Rightarrow y=\frac{1}{4}x+\frac{-1+12}{4}$
$\Rightarrow y=\frac{1}{4}x+\frac{11}{4}$
Hence, the value of slope is wrong.
The correct equation of the line is
$y=\frac{1}{4}x+\frac{11}{4}$
