https://file.aiquickdraw.com/mathbot/file/1727665088447prdso0e4.jpg

The graph in the image represents "Gasoline Usage" with the horizontal axis labeled as "Miles Driven" and the vertical axis labeled as "Gallons in Tank." The problem asks for the average rate of change over the interval [50, 175].

### Steps to solve:
1. **Identify the points on the graph corresponding to x = 50 and x = 175.**
   - At x = 50, the graph shows approximately **11 gallons** in the tank.
   - At x = 175, the graph shows approximately **3 gallons** in the tank.

2. **Average rate of change formula**:  
   The formula for the average rate of change of a function \( f(x) \) over the interval \([x_1, x_2]\) is:
   \[
   \text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
   \]
   In this case:
   \[
   \text{Average rate of change} = \frac{3 - 11}{175 - 50} = \frac{-8}{125} = -0.064
   \]

### Interpretation:
The average rate of change is approximately **-0.064 gallons per mile**, which matches option D in the multiple-choice list.

### Answer:
The correct answer is **-0.064 gallons/mile**.

Would you like more details or have any questions?

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Here are some related questions to expand your understanding:
1. How do you interpret a negative rate of change in the context of this graph?
2. How would you calculate the rate of change over a different interval, like [25, 150]?
3. What does the slope of the line represent in this gasoline usage graph?
4. How can you determine the total distance the car can travel before running out of fuel?
5. How would the graph change if the car's fuel efficiency improved?

**Tip**: The average rate of change is the slope of the line connecting two points. In real-world problems like this, the slope often represents efficiency, consumption, or speed!

According to the graph, what is the average rate of change over the interval [50, 175]?

Calculate the average rate of change in gasoline usage over the interval [50, 175] miles driven. This solution covers the use of the slope formula, key algebraic concepts, and graph interpretation. Suitable for students in Grades 9-10.

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