Question

consider the graph to the right.
a. in words, describe the function shown on the graph
b. find the slope of the graph and express it as a rate of change.
c. briefly discuss the conditions under which a linear function is a realistic model for the given situation.

rate of change = \\(-87.5\\) miles per hour
(round to the tenths place as needed.)

c. select the correct answer below.

a. it is a good model if speed is changing for two hours, then afterwards is constant.
b. it is a good model if speed is constant for two hours and afterwards is changing.
c. it is a good model if speed is constant for 8 hours.
d. it is a good model if speed is not constant for 8 hours.

Explanation:

Analyze the graph and situation

Using the Graph Interpretation knowledge point

$$
LATEXBLOCK0
$$

Interpret the rate of change

Using the Rate of Change Interpretation knowledge point

$$
LATEXBLOCK1
$$

Evaluate the modeling conditions

For a linear function to model this trip realistically, the rate of change (speed) must remain constant throughout the entire duration of the journey. Since the trip takes 8 hours (from \(x = 0\) to \(x = 8\)), the speed must be constant for these 8 hours.

Select the correct option

Comparing the conditions to the multiple-choice options:

• Option A: Speed changes for two hours, then is constant. (Incorrect)
• Option B: Speed is constant for two hours, then changes. (Incorrect)
• Option C: It is a good model if speed is constant for 8 hours. (Correct)
• Option D: It is a good model if speed is not constant for 8 hours. (Incorrect)

Answer:

• A. It is a good model if speed is changing for two hours, then afterwards is constant.
• B. It is a good model if speed is constant for two hours and afterwards is changing.
• C. It is a good model if speed is constant for 8 hours. (Correct answer)
• D. It is a good model if speed is not constant for 8 hours.