Question

1. aaron’s mother drives to the gas station and fills up her tank. then she drives to the market. sketch the graph that shows the relationship between the amount of fuel in the gas tank of her car and time.

y
fuel (gal)
x
time (min)

Explanation:

Step1: Analyze driving to gas station

When driving to the gas station, the car uses fuel, so the fuel amount (y) decreases as time (x) increases. This is a decreasing line segment.

Step2: Analyze filling the tank

While filling the tank, time passes but fuel increases rapidly (since filling is a quick process of adding fuel), so this is a vertical or steeply increasing line segment (fuel rises, time moves forward a bit).

Step3: Analyze driving to market

After filling, driving to the market uses fuel again, so fuel amount decreases as time increases, another decreasing line segment, with a starting fuel level higher than the initial (before filling) end level.

To sketch:

• Start with some initial fuel level, draw a decreasing line (driving to gas station).
• Then, at the time of reaching the gas station, draw a vertical/steep increase (filling tank, fuel goes up to full or desired level).
• Then draw a decreasing line (driving to market) from the new higher fuel level, with slope similar or same as the first decreasing line (assuming constant speed, so constant fuel consumption rate).

Answer:

The graph has three phases: 1) Decreasing line (driving to gas station), 2) Steeply increasing line (filling tank), 3) Decreasing line (driving to market), with the second phase's start at the end of the first, and the third phase's start at the end of the second (higher fuel level than first phase's end).