Final answer:
The relationship between the amount of fuel remaining in Carl's truck's tank and the distance driven is a linear one, described by the equation F = 400 - 0.8D. To graph this relationship, plot the distance on the x-axis, the fuel on the y-axis, and draw a line with a slope of -0.8 starting at (0, 400), indicating a full tank with no kilometers driven.
Step-by-step explanation:
To graph the relationship between the amount of fuel remaining in Carl's truck's tank and the distance driven in kilometers, we need to set up an equation based on the given information.
Let's let F represent the amount of fuel remaining in the tank (in liters) and D represent the distance driven (in kilometers).
We start with 400 liters of fuel, and the truck uses 0.8 liters for each kilometer driven. Thus, the fuel remaining after driving for a certain distance will be:
F = 400 - 0.8D
When D is 0 (meaning the truck hasn't started driving), F is 400 (the tank is full). The relationship between F and D is a linear one, with a slope of -0.8 (the rate of fuel consumption).
Graphing the Relationship:
- On the horizontal axis (x-axis), we plot the distance driven, D, in kilometers.
- On the vertical axis (y-axis), we plot the amount of fuel remaining, F, in liters.
- We plot the point (0, 400) to represent a full tank before the journey begins.
- We can then draw a straight line with a slope of -0.8 decreasing from left to right, to represent the fuel consumption over distance driven.
This graph would show a line descending from (0, 400) moving down and to the right, indicating that as the distance (D) increases, the fuel remaining (F) decreases. The graph will cross the x-axis at the point where the fuel is completely used up, which is the solution to the equation when F = 0:
D = 500 km. This is where the truck would run out of fuel, according to the consumption rate provided.