Question

finding the slope of a line from a table
the table shows the gallons of fuel remaining after a car travels a certain distance in miles

distance (miles)\tfuel remaining (gallons)
0\t13.50
1\t13.46
2\t13.42
3\t13.38
4\t13.34
5\t13.30

the change in fuel remaining from one row to the next in the table is ______ (gallons)
the change in distance from one row to the next in the table is ______ (miles)
the slope of the line that runs through the points given in the table is ______
the slope indicates a ______

Explanation:

Step1: Calculate fuel change per row

Subtract consecutive fuel values: $13.45 - 13.50 = -0.05$

Step2: Calculate distance change per row

Subtract consecutive distance values: $1 - 0 = 1$

Step3: Compute slope (rise over run)

Slope = $\frac{\text{Change in Fuel}}{\text{Change in Distance}} = \frac{-0.05}{1} = -0.05$

Step4: Interpret the slope

Negative slope means fuel decreases as distance increases.

Answer:

The change in fuel remaining from one row to the next in the table is $\boldsymbol{-0.05}$ gallons.
The change in distance from one row to the next in the table is $\boldsymbol{1}$ mile(s).
The slope of the line that runs through the points given in the table is $\boldsymbol{-0.05}$.
The slope indicates a $\boldsymbol{decrease\ of\ 0.05\ gallons\ of\ fuel\ per\ mile\ traveled}$.