Question

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?

Answer 1

His mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31.

i.e. for a linear function, the y values should have a constant rate of change and not the differences.