A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. 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. (2 points)

a
f(x) = −3x + 45

b
f(x) = 3x + 45

c
f(x) = −3x + 60

d
f(x) = 3x + 60

Question

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. 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. (2 points)

a
f(x) = −3x + 45

b
f(x) = 3x + 45

c
f(x) = −3x + 60

d
f(x) = 3x + 60

Vocaloid · Answer

let's let weeks be the independent variable (x) and let the loads of waste removed be the dependent variable (y)

In week 5, there were 45 dumpster loads of waste removed ---> so week 5, 45 loads ---> x = 5, y = 45, which can be represented by the point (5,45)

similar logic with week 10 (10,30)

use the slope formula to calculate the slope between (5,45) and (10,30). once you have the slope (m), you can use the point-slope formula y - y1 = m(x-x1), plug in the slope, as well as either of the original points as your x1, y1, and solve for y to get the final equation