Question

the table shows the amount of gas in mr. orbisons tank, y, as a function of the driving time (h), x.

driving time (h), x	0	1	2	3

1. describe the initial value of the function.

the initial value is 27. it represents the amount of gas in the tank before driving.

1. describe the rate of change of the function.

the rate of change is blank. it represents the amount of gas in the tank with each hour mr. orbison drives.
(there is a dropdown with 7 as an option here, likely for the rate of change calculation.)

Explanation:

Step1: Calculate the rate of change

The rate of change (slope) \(m\) of a linear function is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,27)\) and \((x_2,y_1)=(1,25)\).

$$m=\frac{25 - 27}{1-0}=\frac{- 2}{1}=-2$$

Answer:

The rate of change is \(-2\). It represents the amount of gas decreasing in the tank with each hour Mr. Orbison drives.