Question

What are the rate of change and the initial value of the function represented by the graph?

The rate of change is 3 and the initial value is 5.


The rate of change is 13 and the initial value is 5.


The rate of change is 5 and the initial value is 3.


The rate of change is 5 and the initial value is 13.

Answer 1

Answer: c

Explanation:

Answer 2

The rate of change is 1/3 and the initial value is 5.

Explanation:

See attachment for graph

First, we select any two corresponding x and y values

`(x_1,y_1) = (0,5)`

`(x_2,y_2) = (9,8)`

This implies the slope and slope (m) is calculated as follows:

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

`m = (8-5)/(9-0)`

`m = (3)/(9)`

Simplify

`m = (1)/(3)`

(b) Calculating the initial value.

This is the point
`where\ x = 0`

From the graph, we have the following point:

`(x_1,y_1) = (0,5)`

Here, we have that:

`x = 0` and
`y = 5`

This means the the initial value is 5