Question

Drew and Joel participated in a 4-mile race and plotted their progress on the given graphs. Which of the following statements is incorrect?

• A. Drew and Joel both ran 4 miles.
• B. Drew’s speed is linear from 20 to 40 minutes.
• C. Joel’s graph shows a linear function throughout.
• D. Joel won the race by 5 minutes.

Answer 1

The correct option is C Joel’s graph shows a linear function throughout.

Let’s check each option and compare it with the given graphs.

Option a and b:

• Drew covered 4 miles in 40 minutes, and Joel covered 4 miles in 35 minutes.
• This also tells us that Joel took 5 minutes (40 − 35 = 5 min) less than Drew to complete the race.
• Hence, Joel won the race by 5 minutes.

Therefore, option a and option b are correct.

Option c: Drew’s speed is linear from 20 to 40 minutes.

• The line segments from 20 minutes to 40 minutes pass through the point (20, 2) and (40, 4).

The graph is a straight line between the given intervals. Hence, it is a linear function.
Hence, option c is correct.

Option d: Joel’s graph shows a linear function throughout.

In a graph, when the rate of change or slope is the same and the graph is a straight line, it is a linear function

• Joel’s graph is not a straight line throughout. Hence, it is not a linear function.

Therefore, option d is incorrect.