Answer:
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 [tex]m=\frac{x_2-x_1}{y_2-y_1}[/tex]
Points are (0,-5) and (1,0) substitute in m.
[tex]m=\frac{1-0}{0-(-5)}[/tex]
[tex]m=\frac{1}{5}[/tex]
Points are (1,0) and (2,5) substitute in m.
[tex]m=\frac{2-1}{5-0}[/tex]
[tex]m=\frac{1}{5}[/tex]
Points are (2,5) and (0,-5) substitute in m.
[tex]m=\frac{0-2}{-5-5}[/tex]
[tex]m=\frac{-2}{-10}[/tex]
[tex]m=\frac{1}{5}[/tex]
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
