Question

The following table shows the values of y for different values of x:

x y
0 –3
1 0
2 3


Which statement best explains whether the table represents a linear function or a nonlinear function?
It represents a linear function because its points are not on a straight line.
It represents a nonlinear function because its points are on a straight line.
It represents a linear function because its points are on a straight line.
It represents a nonlinear function because its points are not on a straight line.

Answer 1

The correct answer is C

Answer 2

C. It represents a linear function because its points are on a straight line.

Step-by-step explanation:

Applying any two of the three points in the table to the following equation, gives us the slope constant "m" which later can be used to determine a linear equation

`(0-(-3)) = m ( 1 - 0)\\m =3\\y -(- 3) = 3(x - 0)\\y = 3x - 3`

The linear function above is valid for all of the points shown in the table and therefore they can be plotted in a straight line.