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Reil [10]
3 years ago
15

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 campgro

und. After 4 h, she is 6 mi from the campground. A graph shows her distance from the campground Y, in miles, after x hours. What is the slope of the graph and what does it represent?
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

-3.5

The distance Rachel covers per hour is 3.5 miles

Step-by-step explanation:

After 2 hours, she is 13 miles from the campground.

After 4 hours, she is 6 miles from the campground.

Let x be the number of hours, y be the number of miles from the campground, then we have two points (2,13) and (4,6).

The equation of the line passing through the points (x_1,y_1) and (x_2,y_2) is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

Substitute:

x_1=2\\ \\y_1=13\\ \\x_2=4\\ \\y_2=6

Hence,

y-13=\dfrac{6-13}{4-2}(x-2)\\ \\y-13=-3.5(x-2)\\ \\y=-3.5x+7+13\\ \\y=-3.5x+20

The slope of the line is -3.5 and it represents that  the distance Rachel covers per hour is 3.5 miles.

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