rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. after 2 h, she is 13…

rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. after 2 h, she is 13 mi from the campground. after 4 h, she is 6 mi from the campground. a graph shows her distance y from the campground, in miles, after x hours. what is the slope of the graph, and what does it represent?\na. 20; rachels initial distance from the campground\nb. -3.5; the rate at which rachels distance from the campground changes per hour\nc. 3.5; rachels initial distance from the campground\nd. 20; rachels final distance from the campground

rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. after 2 h, she is 13 mi from the campground. after 4 h, she is 6 mi from the campground. a graph shows her distance y from the campground, in miles, after x hours. what is the slope of the graph, and what does it represent?\na. 20; rachels initial distance from the campground\nb. -3.5; the rate at which rachels distance from the campground changes per hour\nc. 3.5; rachels initial distance from the campground\nd. 20; rachels final distance from the campground

Answer

Explanation:

Step1: Identify two points

We have two points ((x_1,y_1)=(2,13)) and ((x_2,y_2)=(4,6))

Step2: Use the slope formula

The slope formula is (m = \frac{y_2 - y_1}{x_2 - x_1}) Substitute the values: (m=\frac{6 - 13}{4 - 2}=\frac{-7}{2}=-3.5)

The slope of a distance - time graph represents the rate of change of distance. Here, since the distance from the campground is decreasing as time increases, the slope represents the rate at which Rachel's distance from the campground changes per hour.

Answer:

B. -3.5; the rate at which Rachel's distance from the campground changes per hour