with lines of the form y=mx+b lines are parallel as long as m is the same->m=5
so we know the new line also has the form y=5x+b, so now we have to calculate the b to pass through (4,7)
for this insert x=4, and y=7 to solve for b
7=5*4+b
7=20+b
-13=b
so the parallel line through (4,7) has the equation y=5x-13
