Let's find the answers step-by-step by examining the changes in fuel remaining and distance as given in the table.
### 1. Calculate the change in fuel remaining
To find the change in fuel remaining, subtract the fuel remaining at one distance from the fuel remaining at the next distance. Looking at the first two rows:
- Fuel remaining at 0 miles: [tex]\( 13.50 \)[/tex] gallons
- Fuel remaining at 1 mile: [tex]\( 13.46 \)[/tex] gallons
The change in fuel remaining (ΔFuel) from 0 to 1 mile is:
[tex]\[ 13.46 - 13.50 = -0.04 \text{ gallons} \][/tex]
### 2. Calculate the change in distance
To find the change in distance, subtract the distance at one point from the distance at the next point:
- Distance at point 0: [tex]\( 0 \)[/tex] miles
- Distance at point 1: [tex]\( 1 \)[/tex] mile
The change in distance (ΔDistance) from 0 to 1 mile is:
[tex]\[ 1 - 0 = 1 \text{ mile} \][/tex]
### 3. Calculate the slope of the line
The slope of a line is defined as the change in the y-values divided by the change in the x-values (rise over run). In this context, it is the change in fuel remaining (ΔFuel) divided by the change in distance (ΔDistance):
[tex]\[ \text{Slope} = \frac{\Delta \text{Fuel}}{\Delta \text{Distance}} = \frac{-0.04 \text{ gallons}}{1 \text{ mile}} = -0.04 \text{ gallons per mile} \][/tex]
This means the car consumes 0.04 gallons of fuel per mile traveled.
### 4. Interpretation of the slope
The negative slope indicates a decrease in fuel remaining as the distance increases. This decrease signifies the amount of fuel the car consumes per mile:
[tex]\[ \text{The slope indicates a decrease in fuel consumption per mile.} \][/tex]
Therefore, filling out the table:
```
The change in fuel remaining from one row to the next in the table is -0.04 gallon(s).
The change in distance from one row to the next in the table is 1 mile(s).
The slope of the line that runs through the points given in the table is -0.04.
The slope indicates a decrease in fuel consumption per mile.
```
