Answer:
Third option
m = 2.25
Step-by-step explanation:
The slope of the function is equal to its rate of change between two points.
For example, for a couple of points [tex](x_1, y_1),\ (x_2, y_2)[/tex]
The slope is:
[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]
In this problem we have the following points
1.(2, 8.50) , 2. (5, 15.25), 3. (8, 22.00) , 4. (12, 31.00)
We calculate the slope between the first two points
[tex]m =\frac{15.25-8.50}{5-2}=2.25[/tex]
We calculate the slope between the points 3 and 4
[tex]m =\frac{31-22}{8-4}=2.25[/tex]
We calculate the slope between the points 2 and 3
[tex]m =\frac{22-15.25}{8-5}=2.25[/tex]
The slope is always the same. Therefore m is constant and the fution is a line of slope m = 2.25
