To find the slope of Francis's hike and an equation that represents the scenario, we can use the points given: (1, 100) for the elevation after 1 hour and (5, 360) for the elevation after 5 hours.
-
Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65 \]
-
Use the point-slope form of the equation of a line: The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] We can use either point, but we’ll use the point (1, 100): \[ y - 100 = 65(x - 1) \]
Now we check the choices:
- 65; y−360=65(x−5) (This is not correct since it uses the point (5, 360) and doesn't match the start point)
- 65; y−360=65(x−1) (This is not correct since it uses the slope but the wrong points)
- 65; y−100=65(x−5) (This is not correct as it uses a wrong point)
- 260; y−100=260(x−1) (This is incorrect as the slope should be 65, not 260)
So the correct representation of the slope and the equation is: \[ 65; y - 100 = 65(x - 1) \]
Thus, the correct choice is: 65; y−100=65(x−1).