Question

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.