Question

1. the graph shows the linear relationship between the maximum area in square feet that can be painted and the number of gallons of paint used.

paint coverage
graph of paint coverage with x-axis as number of gallons of paint and y-axis as area painted (ft²), showing a line from (0,0) with a positive slope
what is the rate of change of the area painted with respect to the number of gallons of paint used?
rate of change = ______

Explanation:

Step1: Recall rate of change formula

The rate of change for a linear relationship (slope) is given by $\frac{\text{Change in } y}{\text{Change in } x}$, where $y$ is the area painted and $x$ is the number of gallons.

Step2: Identify two points on the line

From the graph, when $x = 1$ (gallon), $y = 400$ (sq ft); when $x = 2$ (gallons), $y = 800$ (sq ft). Or we can use $(0,0)$ and $(3,1200)$ (since at $x = 3$, $y = 1200$). Let's use $(0,0)$ and $(3,1200)$.

Step3: Calculate rate of change

Using the formula $\frac{y_2 - y_1}{x_2 - x_1}$, substitute $y_2 = 1200$, $y_1 = 0$, $x_2 = 3$, $x_1 = 0$. So $\frac{1200 - 0}{3 - 0}=\frac{1200}{3}=400$.

Answer:

400 square feet per gallon