Question

Which statement best explains whether the table represents a linear or nonlinear function? Input (x) Output (y) 2 5 4 10 6 15 8 20

A It is a linear function because the input values are increasing.

B It is a nonlinear function because the output values are increasing.

C It is a linear function because there is a constant rate of change in both the input and output.

D It is a nonlinear function because there is a constant rate of change in both the input and output.

Answer 1

C It is a linear function because there is a constant rate of change in both the input and output.

Step-by-step explanation:

With the values, you can see that the Y value is always 2.5 times the value of X. That's a constant rate of change.

Answers A and B make no sense, because the fact that the input or output values are increasing or decreasing have no impact to determine if a function is linear or not, can be linear or non-linear in all cases.

Answer D gives the definition of a linear function, but applies it to a non-linear function.

Answer 2

C It is a linear function because there is a constant rate of change in both the input and output.

Explanation:

With the values, you can see that the Y value is always 2.5 times the value of X. That's a constant rate of change.

Answers A and B make no sense, because the fact that the input or output values are increasing or decreasing have no impact to determine if a function is linear or not, can be linear or non-linear in all cases.

Answer D gives the definition of a linear function, but applies it to a non-linear function.