A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed.

Question

(rest of question) In week 10, there were 30 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) = −2x + 40

B: f(x) = 2x + 40

C: f(x) = −2x + 50

D: f(x) = 2x + 50

Answer 1

To start this question, we must first define our variables.

Here, it makes the most sense to have x be the amount of time, and f(x) to be the number of loads of waste removed.

We should write this as a linear equation in the form f(x) = mx+b , where m is the slope and b is the intercept.

f(x) = mx + b

In order for a linear equation to get smaller as time progresses, its slope must be negative.

Luckily, we know how to calculate the slope of a graph, which is given to us by the handy dandy formula: rise/run or (y₂-y₁)/(x₂-x₁). f(x) and y are interchangeable.

So we have a y₂ of 30 and a y₁ of 40, and an x₂ of 10 and a x₁ of 5.

Plugging those numbers into our equation, we get: (30-40)/(10-5), which gives us -2.

So we know that f(x)= -2x+b , but how do we find b?

Worry not! We simply plug known values of f(x) and x given to us by the question!

Let's use the values at 10 weeks. x should be 10, and f(x) should be 30

30 = -2(10) + b

30 = -20 + b

30 + 20 = -20 + 20 + b

50 = b

Now we have all the pieces we need!

f(x) = -2x+50

or

C