Francis is hiking up Ellington Hill. After 1 hour, he is at an elevation of 100 feet. After 5 hours, he is at an elevation of 360 feet. Find the slope and an equation that represents the scenario.(1 point) Responses 65; y−100=65(x−5), 65; y−360=65(x−1), 65; y−360=65(x−5), 260; y−100=260(x−1)

Answer 1

To find the slope and an equation that represents the scenario of Francis hiking, we can follow these steps:

1. Identify the points representing the elevation:

   • After 1 hour, he is at 100 feet: (1, 100)
   • After 5 hours, he is at 360 feet: (5, 360)

2. Calculate the slope (m):
   The slope formula is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (1, 100)\) and \((x_2, y_2) = (5, 360)\).

   Substituting in the values: \[ m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65 \]

3. Formulate the equation using the point-slope form:
   The point-slope equation is: \[ y - y_1 = m(x - x_1) \] Using one of the points, let's use (1, 100): \[ y - 100 = 65(x - 1) \]

Now we can check the response options:

• 65; \(y−100=65(x−5)\) (Incorrect, wrong point)
• 65; \(y−360=65(x−1)\) (Incorrect, wrong point)
• 65; \(y−360=65(x−5)\) (Incorrect, wrong point and elevation)
• 260; \(y−100=260(x−1)\) (Incorrect slope)

The correct answer is: 65; \(y - 100 = 65(x - 1)\)

However, this particular option is not listed. Based on the calculations, you can conclude that the slope is indeed 65 and the equation should be \(y - 100 = 65(x - 1)\). The other equations provided don't match the correct slope or point calculations.