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 minus 1 is equal to 6 , 17 minus 7 is equal to 10 , and 31 minus 17 is equal to 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?
Answer
A
He determined that the differences of 6 , 10 , and 14 are increasing by 4 each time.
B
He concluded that the function has a constant rate of change.
C
He found the differences in the y -values as 7 minus 1 is equal to 6 , 17 minus 7 is equal to 10 , and 31 minus 17 is equal to 14 .
D
He reasoned that a function that has a constant rate of change is linear.
Explanation
The first differences in the y-values are 6, 10, and 14, so they are not constant; they increase by 4. A linear function must have a constant rate of change, meaning equal changes in y for equal changes in x. Willis mistook the constant increase between the differences for a constant rate of change in the function, so his mistake was concluding that the function has a constant rate of change.
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