Question

Which statement best explains whether the table represents a linear or nonlinear function? Input (x) Output (y) −2 7 −5 4 −8 1 −11 −2 It is a linear function because there is a constant rate of change in both the input and output values. It is a nonlinear function because there is a constant rate of change in both the input and output values. It is a linear function because the input values are decreasing. It is a nonlinear function because the input values are increasing.

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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

m= y2-y1/x2-x1 = 10-5/4-2 = 5/2

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.