Francis is hiking up Killington 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)

Question

Responses

65; y−360=65(x−5)
65; y minus 360 equals 65 left parenthesis x minus 5 right parenthesis

65; y−360=65(x−1)
65; y minus 360 equals 65 left parenthesis x minus 1 right parenthesis

260; y−100=260(x−1)
260; y minus 100 equals 260 left parenthesis x minus 1 right parenthesis

65; y−100=65(x−5)

Answer 1

To find the slope and equation of the line representing Francis' hike, we can follow these steps:

1. Identify two points from the given information:

   • After 1 hour: (1, 100)
   • After 5 hours: (5, 360)

2. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where (x₁, y₁) = (1, 100) and (x₂, y₂) = (5, 360). \[ m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65 \]

3. Use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] We can use the point (1, 100): \[ y - 100 = 65(x - 1) \]

Now, let’s see which of the responses matches our findings:

• 65; \( y−100=65(x−1) \) is correct.

Thus, the answer is: 65; y−100=65(x−1)