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.

Answer 1

let x represent the number of week, and y dumpster loads
in `week 5 ` means when x= 5, 60 dumpster loads of waste removed means y=60
x=5 , y=60 ->>> (5,60)

`In week 10, there were 40 dumpster loads removed.` will give you another order pair.
Linear equation in slope intercept form is `y=mx+b` where m represent the slope and b is the y-intercept
use the slope formula to find slope \[\large\rm (\color{Red}{x_1},\color{blue}{y_1})(\color{red}{x_2},\color{blue}{y_2}) \]
\[\large\rm m=\frac{\color{blue}{y_2-y_1}}{\color{red}{x_2-x_1}}\]
To find y-intercept(b):

y=mx+b
replace x and y with one of the order pair( doesn't matter which one u pick), replace m with the slope and solve for b