Question

let g be the number of gallons of gasoline that remain in a cars gasoline tank after the car has been driven d miles since the tank was filled. some pairs of values of d and g are shown in the following table.

d (miles)	g (gallons)
40	9
60	7
80	5
100	3
120	1

complete parts a. to e.
(the upper part on the right has some incomplete text, and then: )
b. the d - intercept of the model is. the d - intercept estimates the number of gallons of gasoline in the tank at the start of the trip.
e. find the g - intercept of the model. what does it mean in this situation?
select the correct choice and fill in the answer box to complete your choice.
(type an ordered pair.)
a. the g - intercept of the model is. the g - intercept estimates the number of gallons of gasoline in the tank at the start of the trip.
b. the g - intercept of the model is. the g - intercept estimates the number of miles after which the gasoline tank will be empty.

Explanation:

Step1: Find the slope of the line

First, we use two points from the table, say \((20, 11)\) and \((40, 9)\). The slope \(m\) is calculated as \(m=\frac{g_2 - g_1}{d_2 - d_1}=\frac{9 - 11}{40 - 20}=\frac{-2}{20}=-0.1\).

Step2: Use point - slope form to find the equation

Using the point - slope form \(g - g_1=m(d - d_1)\) with the point \((20, 11)\) and \(m=-0.1\).
\(g - 11=-0.1(d - 20)\)
\(g - 11=-0.1d + 2\)
\(g=-0.1d+13\)

Step3: Find the g - intercept

The g - intercept occurs when \(d = 0\). Substitute \(d = 0\) into the equation \(g=-0.1d + 13\).
When \(d = 0\), \(g=13\). So the g - intercept is the ordered pair \((0,13)\).
The g - intercept represents the number of gallons of gasoline in the tank when the number of miles driven \(d = 0\) (at the start of the trip). So option A is correct.

Answer:

A. The g - intercept of the model is \((0,13)\). The g - intercept estimates the number of gallons of gasoline in the tank at the start of the trip.