Question

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

Answer 1

General equation of line 
y = mx + c

Since this line is parallel to y=7x-8
m=7

y = 7x + c
If point (5,-2) is in that line,
-2 = (7*5) + c
-2 = 35 + c
c = -37

so the equation is
y = 7x + -37

Answer 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.