Question

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)
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)**