Question

Which statement best explains whether the table represents a linear or nonlinear function?

A.) It is a linear function because there is a constant rate of change in both the input and output values.
B.) It is a nonlinear function because there is a constant rate of change in both the input and output values.
C.) It is a linear function because the input values are decreasing.
D.) It is a nonlinear function because the input values are increasing
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Answer 1

Answer: A.) It is a linear function because there is a constant rate of change in both the input and output values.

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Step-by-step explanation:

Note how x is decreasing by 3 each time

• -2-3 = -5
• -5-3 = -8
• -8-3 = -11

At the same time, y is also decreasing by 3 each time

• 7-3 = 4
• 4-3 = 1
• 1-3 = -2

This means we have a linear function. We have,

slope = (change in y)/(change in x)

slope = (-3)/(-3)

slope = 1

Recall that slope is another term for rate of change, so a constant slope means we have a constant rate of change.

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Another way to find the slope is to pick any two points from the table and use the slope formula

m = (y2 - y1)/(x2 - x1)

You should find that any two points you pick will lead to a slope of 1. I recommend you try out all possible pairs to help convince yourself the slope is 1.