Question

miranda buys a large bag of fertilizer and uses a device to spread the fertilizer across her front yard. the amount of fertilizer miranda has left depends on how much of the lawn she has already covered. this situation can be modeled as a linear relationship. chart: x-axis (lawn covered, square feet) from 0 to 1000, y-axis (fertilizer remaining, pounds) from 0 to 10, line from (0,10) to (1000,0)

Explanation:

Step1: Identify the linear equation form

The general form of a linear equation is \( y = mx + b \), where \( b \) is the y - intercept and \( m \) is the slope. From the graph, when \( x = 0 \) (no lawn covered), \( y = 10 \). So \( b = 10 \).

Step2: Calculate the slope

We can use two points on the line. Let's take \( (0,10) \) and \( (1000,0) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 10}{1000 - 0}=\frac{- 10}{1000}=-0.01 \).

Step3: Write the equation

So the equation of the line is \( y=-0.01x + 10 \), where \( y \) is the amount of fertilizer remaining (in pounds) and \( x \) is the area of the lawn covered (in square feet). If we want to find, for example, the rate at which fertilizer is used, the slope \( - 0.01 \) means that for each square foot of lawn covered, 0.01 pounds of fertilizer is used. Or if we want to find how much lawn is covered when a certain amount of fertilizer is left, we can substitute the value of \( y \) into the equation and solve for \( x \).

Answer:

The linear model is \( y=-0.01x + 10 \) (where \( y \): fertilizer remaining in pounds, \( x \): lawn area covered in square feet)