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Which situation is NOT an example of a linear function?

Responses
A The distance traveled if a car is driving at a constant rate of 60 miles per hour.The distance traveled if a car is driving at a constant rate of 60 miles per hour.
B The cost of the bill if a cell phone company charges an initial fee of $25 plus $45 per month.The cost of the bill if a cell phone company charges an initial fee of $25 plus $45 per month.
C The amount of cake each person gets to eat if a cake is divided equally among the guests at a party.The amount of cake each person gets to eat if a cake is divided equally among the guests at a party.
D The amount of time spent grading papers if a teacher grades one paper every 8 minutes and takes a 10 minute break.The amount of time spent grading papers if a teacher grades one paper every 8 minutes and takes a 10 minute break.

1 answer

To determine which situation is NOT an example of a linear function, we need to consider each option:

A. The distance traveled if a car is driving at a constant rate of 60 miles per hour.

  • This is a linear function because distance = rate × time, which is a linear equation.

B. The cost of the bill if a cell phone company charges an initial fee of $25 plus $45 per month.

  • This is also a linear function, as it can be expressed as C = 25 + 45m, where C is the cost and m is the number of months.

C. The amount of cake each person gets to eat if a cake is divided equally among the guests at a party.

  • This situation could be linear if there is a constant number of guests. If the number of guests varies, the amount of cake per person would be divided among the varying number of guests, but it can still be modeled as a linear function based on the number of guests.

D. The amount of time spent grading papers if a teacher grades one paper every 8 minutes and takes a 10 minute break.

  • This situation introduces a non-linear element because the teacher takes breaks after grading a certain number of papers. The time spent will not increase linearly; it depends on the number of papers graded and includes additional time for breaks.

Based on this analysis, the correct answer is: D. The amount of time spent grading papers if a teacher grades one paper every 8 minutes and takes a 10 minute break.