Question 7 • 2025-2026_MDCPS_1205070-M/J Grade 8 Pre-Algebra Sem 1-CR
Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?xy1127317431
Answer
A
He found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14.
B
He determined that the differences of 6, 10, and 14 are increasing by 4 each time.
C
He concluded that the function has a constant rate of change.
D
He reasoned that a function that has a constant rate of change is linear.
Explanation
The x-values increase by 1 each time, so the rate of change is given by the successive changes in y: 6, 10, and 14. Those changes are not constant, so the function does not have a constant rate of change. Willis’s mistake was concluding that it did; the fact that the changes increase by 4 each time does not make the function linear.
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