The answer would be 45 weeks, since you do 530-80 since that is the part the parents will foot, which will be 450 left. Then you do that divided by 10 since you plan to save 10 dollars a week and therefore are left with 45 weeks.
First move the 14x over to get 7y=-14x-9 then divide by 7 and you get y= -2x-9/7. the slope is the value next to the x in y=mx+b form so the slope is -2