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Take your time on this question. Try to look at the change between the 7.5 gallon mark and the 2.5 gallon mark. The tank started with gallons of gas The rate of change is gallons per hour.

The slope starts at 6, 2 and ends at 0, 7.5

3 answers

To analyze the scenario involving the gas tank, we can break down the information and find the change in the gallons of gas over time.

Understanding the Points

You provided two points:

  • Starting point: (6, 2)
  • Ending point: (0, 7.5)

Points Explained

  • In the coordinates (time, gallons):
    • (6, 2) means that at 6 hours, there are 2 gallons left in the tank.
    • (0, 7.5) means that at 0 hours (the starting point), there are 7.5 gallons of gas in the tank.

Calculating the Change

Now, let's find the change in the gallons of gas from the starting point (0, 7.5) to the ending point (6, 2):

  1. Calculate the Change in Gallons: \[ \text{Change in Gallons} = \text{Final Gallons} - \text{Initial Gallons} = 2 - 7.5 = -5.5 \text{ gallons} \]

  2. Calculate the Change in Time: \[ \text{Change in Time} = \text{Final Time} - \text{Initial Time} = 6 - 0 = 6 \text{ hours} \]

Calculating the Rate of Change (Slope)

The rate of change (slope) can be computed as follows: \[ \text{Slope (Rate of Change)} = \frac{\text{Change in Gallons}}{\text{Change in Time}} = \frac{-5.5 \text{ gallons}}{6 \text{ hours}} \approx -0.9167 \text{ gallons per hour} \]

Summary

The analysis shows that the gallons of gas in the tank decreased from 7.5 gallons to 2 gallons over a period of 6 hours. The rate of change of gas in the tank is approximately -0.9167 gallons per hour, indicating that the tank is being emptied at that rate.

If you have any further questions or need additional clarification, feel free to ask!

I made a mistake, the slope starts at 6, 2 and ends at 0, 8

No problem! Let's analyze the new points provided for the scenario and determine the change in gallons of gas again.

Updated Points

  • Starting point: (6, 2)
  • Ending point: (0, 8)

Points Explained

  • In the coordinates (time, gallons):
    • (6, 2) means that at 6 hours, there are 2 gallons left in the tank.
    • (0, 8) means that at 0 hours (the starting point), there are 8 gallons of gas in the tank.

Calculating the Change

Now we will calculate the change in the gallons of gas from the starting point (0, 8) to the ending point (6, 2):

  1. Calculate the Change in Gallons: \[ \text{Change in Gallons} = \text{Final Gallons} - \text{Initial Gallons} = 2 - 8 = -6 \text{ gallons} \]

  2. Calculate the Change in Time: \[ \text{Change in Time} = \text{Final Time} - \text{Initial Time} = 6 - 0 = 6 \text{ hours} \]

Calculating the Rate of Change (Slope)

The rate of change (slope) can be computed as follows: \[ \text{Slope (Rate of Change)} = \frac{\text{Change in Gallons}}{\text{Change in Time}} = \frac{-6 \text{ gallons}}{6 \text{ hours}} = -1 \text{ gallon per hour} \]

Summary

With the updated points, the gallons of gas in the tank decreased from 8 gallons to 2 gallons over a period of 6 hours. The rate of change of gas in the tank is -1 gallon per hour, indicating that the tank is being emptied at that rate.

If you have any further questions or would like to explore more about this scenario, feel free to ask!