Question

aldo is driving on the highway. he begins the trip with 12 gallons of gas in his car. the car uses up one gallon of gas every 25 miles. let g represent the number of gallons of gas he has left in his tank, and let d represent the total distance (in miles) he has traveled. (a) write an equation relating g to d. equation: (b) graph your equation using the axes below.

Explanation:

Step1: Define gas used per mile

The car uses $\frac{1}{25}$ gallons per mile.

Step2: Calculate gas used for distance $D$

Gas used = $\frac{D}{25}$

Step3: Relate remaining gas to distance

Remaining gas $G$ starts at 12, minus gas used.
$G = 12 - \frac{D}{25}$

Step4: Identify graph intercepts

• G-intercept (when $D=0$): $G=12$
• D-intercept (when $G=0$): $0=12-\frac{D}{25} \implies D=300$

Plot the line connecting (0, 12) and (300, 0), only for non-negative $G$ and $D$.

Answer:

(a) $G = 12 - \frac{D}{25}$
(b) Graph: Draw a straight line connecting the points $(0, 12)$ (on the G-axis) and $(300, 0)$ (on the D-axis), with the line only extending in the first quadrant (since distance and gas cannot be negative).