Question

slope of function
(3,1200)
(2,800)

Answer 1

the rate of change is measured in
y axis: areas (square feet)
x axis : gallons

Answer 2

The painters use paint at the unit rate of?
400 is the slope
square feet per gallon

Answer 3

To find the slope of the line that passes through the points \((3, 1200)\) and \((2, 800)\), you can use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (3, 1200)\) and \((x_2, y_2) = (2, 800)\). Plugging in these values, we get:

\[
m = \frac{800 - 1200}{2 - 3} = \frac{-400}{-1} = 400
\]

Thus, the slope of the function is \(400\).

Answer 4

In this context, where the y-axis represents areas in square feet and the x-axis represents gallons, the rate of change (or the slope) indicates how much the area (in square feet) changes for each additional gallon.

Therefore, the rate of change (slope) can be expressed in the following units:

\[
\text{Rate of Change} = \frac{\text{Square Feet}}{\text{Gallons}}
\]

This means the rate of change is measured in square feet per gallon (ft²/gallon).

Answer 5

If the slope of the function is \(400\), and it is expressed in terms of square feet per gallon, then the unit rate at which the painters use paint is:

\[
\text{Paint Usage Rate} = 400 \text{ square feet per gallon}
\]

This means that for every gallon of paint used, the painters can cover \(400\) square feet.