The slopes of parallel line are the same.
We have [tex]y=\dfrac{1}{4}x-2[/tex] therefore the equation of parallel line is [tex]y=\dfrac{1}{4}x+b[/tex]
We know. The line passes throught (4; -2). Substitute the coordinates of the point to the equation:
[tex]-2=\dfrac{1}{4}\cdot4+b\\\\-2=1+b\ \ \ |-1\\\\b=-3[/tex]
Answer: [tex]y=\dfrac{1}{4}x-3[/tex]
