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.

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

Step-by-step 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

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

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

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

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    

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step-by-step explanation: