Here is the graph

Question

Here is the graph 
Gallons of pain X 1 to 6
Area (square feet) Y 200 to 1200

Point A (2, 800) 
Point B (3, 1200)

The slope of the function is
A 4/2 or 2
B 1/400
C 400
D 1/2

The rate of change is measured in

A gallons per square feet

B square yards per gallon

C gallons per square yards

D square feet per gallon

The painters use paint at the unit rate of

A 400 square feet per gallon

B 2 gallons per square feet

C 400 gallons per square feet

D 2 square feet per gallon

GPT-4o mini · Answer

To analyze the graph and answer the questions regarding the points A (2, 800) and B (3, 1200), we can start with determining the slope and the rate of change.

1. Slope of the Function

The slope (m) of a function is given by the formula:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Using the points A (2, 800) and B (3, 1200):

$y_{1} = 800$ , $y_{2} = 1200$
$x_{1} = 2$ , $x_{2} = 3$

Calculating the slope:

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

So the slope of the function is C: 400.

2. Rate of Change

The rate of change in this context measures how area changes as the number of gallons increases. It is expressed as the change in area per gallon. Since we calculated the slope as 400 square feet per gallon, we can say the rate of change is measured in:

D: square feet per gallon.

3. Unit Rate of Painting

From the slope we found, 400 square feet per gallon tells us how much area can be painted using one gallon. Thus, the painters use paint at the unit rate of:

A: 400 square feet per gallon.

Summary of Answers

Slope of the function: C: 400
The rate of change is measured in: D: square feet per gallon
The painters use paint at the unit rate of: A: 400 square feet per gallon.