Question

1. paola is mulching her flower garden. she was able to mulch 48 square feet of garden before lunch. she plans to finish the job after lunch. each bag of mulch covers 24 square feet of garden.

a. write an equation that represents the number of square feet of garden, y, given x number of bags of mulch.
b. graph the equation.
c. identify the slope and y - intercept of the graph. explain what each means in terms of the situation.
d. if paola has 4 bags of mulch still after lunch. how many square feet of her garden will she be able to mulch?

Explanation:

Step1: Determine the equation

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.
Paola mulched 48 square feet before lunch (\(b = 48\)). Each bag covers 24 square feet (\(m = 24\)).
So the equation is \(y=24x + 48\).

Step2: Identify slope and \(y\)-intercept

For the equation \(y = 24x+48\), the slope \(m = 24\). In the context, it means that each bag of mulch covers 24 square feet of the garden.
The \(y\)-intercept \(b = 48\). It means that before lunch (when \(x = 0\) bags used after lunch), 48 square feet of the garden was already mulched.

Step3: Calculate for \(x = 4\)

Substitute \(x = 4\) into the equation \(y=24x + 48\).
\(y=24\times4+48\)
\(y = 96+48\)
\(y=144\)

Answer:

a. \(y = 24x+48\)
c. Slope \(m = 24\) (each bag covers 24 square - feet), \(y\)-intercept \(b = 48\) (48 square - feet mulched before lunch)
d. 144 square feet