https://file.aiquickdraw.com/mathbot/file/17297980864622119lnpc.jpg

Let's analyze the problem step by step:

Karl's truck starts with 400 liters of fuel, and the truck consumes 0.8 liters of fuel per kilometer driven. The relationship between the remaining fuel \( F \) and the distance driven \( D \) (in kilometers) can be modeled by the linear equation:

\[
F = 400 - 0.8D
\]

This is a straight line with:
- A y-intercept of 400 liters (the initial fuel).
- A slope of \(-0.8\), indicating that for every kilometer driven, 0.8 liters of fuel are used.

Now, let’s examine the graphs. We are looking for a graph that:
1. Starts at 400 liters of fuel when 0 kilometers have been driven.
2. Decreases at a rate of 0.8 liters per kilometer, meaning the graph should have a negative slope.
3. Reaches 0 liters of fuel after \( D = \frac{400}{0.8} = 500 \) kilometers.

From the graphs in the image:
- The second graph (which is already selected) shows a line starting at 400 liters and reaching 0 liters after 500 kilometers, which fits the equation.

Thus, the second graph is the correct representation.

Would you like more details on the calculations or have any questions?

Here are 5 related questions:
1. How would the graph change if the fuel consumption increased to 1 liter per kilometer?
2. What would the slope of the line be if the fuel consumption decreased to 0.5 liters per kilometer?
3. How many kilometers could the truck drive if it started with 200 liters of fuel?
4. If the truck drove 250 kilometers, how much fuel would remain?
5. What is the significance of the y-intercept in this scenario?

**Tip:** Always verify units (like kilometers and liters) to ensure they match when analyzing real-world problems.

Karl filled up the tank of his truck with 400 Liters of fuel and set out to deliver a shipment of bananas to Alaska. The truck consumed 0.8 liters of fuel for each kilometer driven. Which of the following graphs shows the relationship between the amount of fuel remaining in the truck's tank (in liters) and distance driven (in kilometers)?

Explore the linear relationship between the fuel remaining in Karl's truck and the distance driven. Using the equation F = 400 - 0.8D, learn how to interpret the slope and graph a real-world problem. This problem is suitable for students in Grades 8-10.

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