Question

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

x y

0 -5

1 0

2 5




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

It represents a linear function because it's points are on a straight line

It represents a linear function because it's points are not on a straight line


It represents a nonlinear function because its points are on a straight line

It represents a nonlinear function because it's points are not on as straight line.

Answer 1

A. It represents a linear function because it's points are on a straight line the equation is y=5x-5

Answer 2

Option 1 - It represents a linear function because it's points are on a straight line

Explanation:

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

x y

0 -5

1 0

2 5

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

Solution :

For a linear equation the slopes of the line between any two pairs of these is the same.

For a non-linear equation the slopes of the line between any two pairs of these is different.

First we find the slope,

Slope is
`m=(x_2-x_1)/(y_2-y_1)`

Points are (0,-5) and (1,0) substitute in m.

`m=(1-0)/(0-(-5))`

`m=(1)/(5)`

Points are (1,0) and (2,5) substitute in m.

`m=(2-1)/(5-0)`

`m=(1)/(5)`

Points are (2,5) and (0,-5) substitute in m.

`m=(0-2)/(-5-5)`

`m=(-2)/(-10)`

`m=(1)/(5)`

The slopes are same, so it is a linear function.

The points are also in a straight line as shown in figure attached below.

Therefore, Option 1 is correct.

It represents a linear function because it's points are on a straight line