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 trash removed and 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​

Answer 1

Answer:

y = -3x + 60, D: x ≥ 0, r: y ≥ 0

Step-by-step explanation:

1. Find the slope (x-axis is the week number, y-axis is the # of dump loads)

Slope equation: (y₁ - y₂)/(x₁ - x₂), where two points are (x₁, y₁) and (x₂, y₂)

Plug in: (45 - 30)/(5 - 10)

Subtract: 15/(-5)

Divide: -3, representing the number of dumps removed/week

2. Find the y-intercept (when x = 0)

Since we found that 3 dumps are removed per week, we can find that at week 0, there were 60 dump loads.

3. Construct equation

Point-intercept equation: y = mx + b, where m = slope, b = y-intercept

Plug in: y = -3x + 60 (with the domain of x ≥ 0 and the range of y ≥ 0)