Question

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 60 dumpster loads of waste removed. In week 10, there were 40 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. a. f(x) = - 4x + 60. b. f(x) = 4x + 60. c. f(x) = - 4x + 80. d. f(x) = 4x + 80

Answer 1

The correct answer is c) f(x) = -4x+80.

We first find the rate of change, or slope, between points. The two points we are given are
(5, 60) and (10, 40)

We find the slope using the formula
m = (y₂ - y₁)/(x₂ - x₁) = (40-60)/(10-5) = -20/5 = -4

Now we put this in point-slope form, which is
y-y₁ = m(x-x₁)
y-60 = -4(x-5)

Using the distributive property,
y-60 = -4*x --4*5
y-60 = -4x+20

Add 60 to both sides:
y-60+60 = -4x+20+60
y = -4x+80