https://file.aiquickdraw.com/mathbot/file/1733884094091q386pc3i.jpg

From the image provided, the task is to find the rate of change (slope) from the graph, which represents the relationship between the number of gallons of gas and the miles driven by Nabhitha.

The slope or rate of change is calculated as:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph, we can observe two points:
1. \( (10, 394) \)
2. \( (20, 788) \)

Substitute these values into the slope formula:

\[
\text{slope} = \frac{788 - 394}{20 - 10} = \frac{394}{10} = 39.4
\]

### Conclusion:
The rate of change is **39.4 miles per gallon**, meaning Nabhitha can drive 39.4 miles for every gallon of gas.

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Would you like a deeper explanation or help with a related topic?  
Here are five questions you might explore next:

1. What does a linear relationship imply in this graph?
2. How is the slope related to fuel efficiency in real-world terms?
3. What units does the slope represent, and why is it important to consider them?
4. How would you find the total miles driven if you knew a specific amount of gas used?
5. How can you verify the accuracy of the points used to calculate the slope?

**Tip:** Always label your units clearly when interpreting slopes or rates of change—they provide critical context for understanding real-world problems.

The graph below represents the number of miles, y, that Nabhitha can drive her car for every x gallons of gas. Find the rate of change.

Learn how to calculate the rate of change for Nabhitha's gas mileage from a graph showing miles driven versus gallons of gas. Understand the slope formula with real-world application, where the rate of change is 39.4 miles per gallon. Suitable for middle school students in Grades 6-8.

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