What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

Let the equation of the given line be y=mx+a. This line has slope m and the parallel line will have the same slope.
Then the equation of the parallel line to the line y=mx+a will be y=mx+b. Since line passes through the point (–2, 2), the coordinates of this point suit the equation:

2=m·(-2)+b,
2=-2m+b,
b=2+2m 
and the equation is y=mx+2m+2. 
You should only to paste correct m from the given equation.