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 trash removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of trash each week is linear. write an equation in function form to show the amount of trash removed each week.

○ a. f(x)= -4x + 80
○ b. f(x)= 4x + 80
○ c. f(x)= -4x + 50
○ d. f(x)= 4x + 50

Explanation:

Step1: Identify the slope - intercept form

The linear function is of the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate the slope $m$

We have two points $(x_1,y_1)=(5,60)$ and $(x_2,y_2)=(10,40)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{40 - 60}{10 - 5}=\frac{-20}{5}=-4$.

Step3: Find the y - intercept $b$

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(5,60)$ and $m=-4$.
$y-60=-4(x - 5)$
$y-60=-4x + 20$
$y=-4x+80$.

Answer:

A. $f(x)=-4x + 80$