Let's break down the information in the image.

Graph and Problem Overview:

The graph depicts the relationship between the number of gallons of gas consumed (x-axis) and the distance driven (y-axis). The slope of the line represents the car's mileage, meaning how many miles the car can travel per gallon of gas.

• Slope Interpretation: The slope of the graph represents the car's mileage, specifically miles per gallon.

  • This is confirmed by the correct answer to the first question: (A) The approximate mileage of the trip (in miles per gallon).

• Evaluation of f(30): The function f(x) represents the distance driven after consuming x gallons of gas. The calculation of f(30) gives 568, which means:

  • After consuming 30 gallons of gas, the car has traveled 568 miles.

Answer to the second question:

The best interpretation of the result of evaluating f(30) is:

• (B) After using 30 gallons of gas, the car will have traveled 568 miles.

This interpretation matches the function f(x) = distance driven in miles as a function of gallons of gas consumed.

Would you like to dive deeper into the details of how the slope was calculated or explore related concepts? Here are five additional questions to deepen your understanding:

1. How is the slope of the line determined from the graph, and what does it represent in this scenario?
2. What is the equation of the line based on the given points in the graph?
3. How could we use the slope to predict the distance traveled for any given number of gallons of gas?
4. What would happen if the graph were non-linear? How would that affect the mileage interpretation?
5. How would you calculate the average mileage if the car consumed 50 gallons of gas?

Tip: In real-world applications, understanding the slope of a graph can help you determine rates, such as speed or fuel efficiency.