Question

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

x −2 −1 0 1 2
y −4 −2 0 2 −2

The table represents a nonlinear function because there is not a constant rate of change in the output values.

The table represents a nonlinear function because there is not a constant rate of change in the input and output values.

The table represents a linear function because there is a constant rate of change in the input and output values.

The table represents a linear function because there is not a constant rate of change in the input and output values.

Answer 1

The table represents a linear function because the rate of change is constant or all the points lie on a straight line.

Explanation:

From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).

The slope of the line is

The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.

From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.

Since the rate of change (slope) is same for all points, therefore the table represents a linear function.

If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.