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? x

y

1

1

2

7

3

17

4

31

He found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14.

He determined that the differences of 6, 10, and 14 are increasing by 4 each time.

He concluded that the function has a constant rate of change.

He reasoned that a function that has a constant rate of change is linear.