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.

a. select the correct answer below
a. according to the function, the distance from home increases by 700 miles every 8 hours.
b. according to the function, the distance from home increases by 8 miles every 700 hours.
c. according to the function, the distance from home decreases by 700 miles every 8 hours.
d. according to the function, the distance from home decreases by 8 miles every 700 hours.

Explanation:

Analyze the graph axes and initial values

Using the Graph Interpretation knowledge point

$$
LATEXBLOCK0
$$

Determine the behavior of the function

Using the Linear Growth knowledge point

$$
LATEXBLOCK1
$$

Match with the multiple-choice options

We evaluate the given options based on our findings:

• Option A states the distance increases by 700 miles every 8 hours (incorrect, it decreases).
• Option B states the distance increases by 8 miles every 700 hours (incorrect).
• Option C states the distance decreases by 700 miles every 8 hours (correct, as the distance goes from 700 to 0 over 8 hours).
• Option D states the distance decreases by 8 miles every 700 hours (incorrect).

Answer:

• (A) According to the function, the distance from home increases by 700 miles every 8 hours.
• (B) According to the function, the distance from home increases by 8 miles every 700 hours.
• (C) According to the function, the distance from home decreases by 700 miles every 8 hours. (Correct answer)
• (D) According to the function, the distance from home decreases by 8 miles every 700 hours.