What is the equation of a line parallel to y = 7x-8 that passes through (5,-2)

If the line is parallel, the slope is the same, but it's final term will be different. Since slope is the same, just go down 7 and left 1 from (5, - 2) until you reach the y-axis, which will be at y=-9. This is your "b" term, since the equation is in y=mx+b form. So, your equation is y=7x-9.