To solve this problem, let's go through each part step by step:
### Step 1: Finding the change in fuel remaining
First, we need to find the change in fuel remaining from one row to the next in the table. This is done by subtracting the fuel remaining at one distance from the fuel remaining at the previous distance.
Given:
- Fuel remaining at 0 miles = 13.50 gallons
- Fuel remaining at 1 mile = 13.46 gallons
So, the change in fuel remaining from 0 miles to 1 mile is:
[tex]\[ \Delta \text{Fuel} = 13.46 \text{ gallons} - 13.50 \text{ gallons} = -0.04 \text{ gallons} \][/tex]
Thus:
[tex]\[ \text{The change in fuel remaining from one row to the next in the table is } -0.04 \text{ gallon(s)}. \][/tex]
### Step 2: Finding the change in distance
Next, we need to find the change in distance from one row to the next in the table. This is done by subtracting the distance at one row from the distance at the previous row.
Given:
- Distance at 0 miles = 0 miles
- Distance at 1 mile = 1 mile
So, the change in distance from 0 miles to 1 mile is:
[tex]\[ \Delta \text{Distance} = 1 \text{ mile} - 0 \text{ miles} = 1 \text{ mile} \][/tex]
Thus:
[tex]\[ \text{The change in distance from one row to the next in the table is } 1 \text{ mile(s)}. \][/tex]
### Step 3: Calculating the slope of the line
The slope of a line (m) through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the [tex]\(y\)[/tex] values correspond to the fuel remaining and the [tex]\(x\)[/tex] values correspond to the distance traveled.
Given:
- [tex]\(\Delta \text{Fuel} = -0.04 \text{ gallons}\)[/tex]
- [tex]\(\Delta \text{Distance} = 1 \text{ mile}\)[/tex]
So, the slope is:
[tex]\[ \text{Slope} = \frac{-0.04 \text{ gallons}}{1 \text{ mile}} = -0.04 \text{ gallons per mile} \][/tex]
Thus:
[tex]\[ \text{The slope of the line that runs through the points given in the table is } -0.04 \][/tex]
### Step 4: Interpreting the slope
A negative slope indicates that the quantity on the vertical axis (fuel remaining) is decreasing as the quantity on the horizontal axis (distance) increases.
Thus:
[tex]\[ \text{The slope indicates a decreasing trend.} \][/tex]
### Complete Answer
The change in fuel remaining from one row to the next in the table is [tex]\(-0.04\)[/tex] gallon(s).
The change in distance from one row to the next in the table is [tex]\(1\)[/tex] mile(s).
The slope of the line that runs through the points given in the table is [tex]\(-0.04\)[/tex].
The slope indicates a decreasing trend.
