To find the slope of the graph that represents Rachel's distance from the campground over time, we can use the data points provided (time, distance from the campground):
- After 2 hours, she is 13 miles from the campground. This gives us the point (2, 13).
- After 4 hours, she is 6 miles from the campground. This gives us the point (4, 6).
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using our points:
- \( (x_1, y_1) = (2, 13) \)
- \( (x_2, y_2) = (4, 6) \)
Substituting these into the slope formula:
\[ m = \frac{6 - 13}{4 - 2} = \frac{-7}{2} = -3.5 \]
The slope of the graph is \(-3.5\).
Interpretation of the slope: The slope of \(-3.5\) represents Rachel's average rate of change in her distance from the campground per hour. Specifically, it means that for each hour that passes, Rachel gets 3.5 miles closer to the campground. The negative sign indicates that her distance from the campground is decreasing as she hikes toward it.
Overall, the slope can be interpreted as her hiking speed towards the campground as a distance reduction.
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