Question

the table shows the amount of gas in mr. orbisons tank, y, as a function of the number of hours he drives, x. initial value: 27 rate of change: -2 let x equal mr. orbisons driving time, in hours. write an equation to represent the total amount of gas in the tank, y. driving time (h), x | gas in tank (gal), y 0 | 27 1 | 25 2 | 23 3 | 21

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the rate of change (slope) and \(b\) is the initial value (y - intercept).

Step2: Identify the values of \(m\) and \(b\)

Given that the rate of change \(m=-2\) and the initial value \(b = 27\).

Step3: Substitute \(m\) and \(b\) into the equation

Substitute \(m=-2\) and \(b = 27\) into \(y=mx + b\). We get \(y=-2x + 27\).

Answer:

\(y=-2x + 27\)