Answer:
The rate of change is 1/3 and the initial value is 5.
Step-by-step explanation:
See attachment for graph
First, we select any two corresponding x and y values
[tex](x_1,y_1) = (0,5)[/tex]
[tex](x_2,y_2) = (9,8)[/tex]
This implies the slope and slope (m) is calculated as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8-5}{9-0}[/tex]
[tex]m = \frac{3}{9}[/tex]
Simplify
[tex]m = \frac{1}{3}[/tex]
(b) Calculating the initial value.
This is the point [tex]where\ x = 0[/tex]
From the graph, we have the following point:
[tex](x_1,y_1) = (0,5)[/tex]
Here, we have that:
[tex]x = 0[/tex] and [tex]y = 5[/tex]
This means the the initial value is 5
