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.
c. estimate the number of miles driven since the tank was last filled if 4 gallons of gasoline remain in the tank.
the driver drove 90 miles since the tank was last filled if 4 gallons of gasoline are in the tank.
d. find the d-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 d-intercept of the model is. the d-intercept estimates the number miles after which the gasoline tank will be empty.
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.

Explanation:

Step1: Find the linear model

First, we find the slope \( m \) of the line. Using two points, say \( (20, 11) \) and \( (40, 9) \), the slope \( m=\frac{9 - 11}{40 - 20}=\frac{-2}{20}=-0.1 \). The linear equation is \( g - g_1=m(d - d_1) \). Using \( (20, 11) \), we get \( g - 11=-0.1(d - 20) \), which simplifies to \( g=-0.1d + 13 \).

Step2: Find the d - intercept

The d - intercept occurs when \( g = 0 \) (since we want to find when the gasoline tank is empty, \( g = 0 \)). Set \( g = 0 \) in the equation \( 0=-0.1d+13 \). Solving for \( d \):

$$
LATEXBLOCK0
$$

So the d - intercept is \( (130,0) \). Option A is correct because the d - intercept is the number of miles after which the gasoline tank will be empty (when \( g = 0 \)).

Answer:

A. The d - intercept of the model is \( (130,0) \). The d - intercept estimates the number miles after which the gasoline tank will be empty.