Question

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 50 dumpster loads of waste romoved. In week 10, there were 40 dumpster loads removed. Assume that the reduction in the amount of each week is linear. Write an equation in function form to show the amount of trash removed each week

F(x)=2x+60
F(x)=-2x+60
F(x)=-2x+80
F(x)=2x+80

Answer 1

Since we see that the number of dumpster loads of waste removed goes down as weeks go by, that indicates that our slope is negative, which eliminates the first and second options. Now, plug in the number 5 for x, which stands for the week number. When we do it for the third equation we see that -2(5)+80=70, which is not 50 dumpster loads. The only equation we have left is the second, so plug in 5. -2(5)+60= 50, so that checks out. Now plug in week 10, -2(10)+60=40, so that also checks out. Your answer will be equation 2