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:
[tex]y=mx+b[/tex]Since we know the slope, we can write:
[tex]y=\frac{1}{4}x+b[/tex]It passes through (-8,2). So we plug into x and y and find b:
[tex]\begin{gathered} y=\frac{1}{4}x+b \\ 2=\frac{1}{4}(-8)+b \\ 2=-2+b \\ b=2+2 \\ b=4 \end{gathered}[/tex]So, the equation of the lline parallel would be:
[tex]y=\frac{1}{4}x+4[/tex]