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−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)
65; y minus 100 equals 65 left parenthesis x minus 5 right parenthesis

65; y−360=65(x−5)

Answer 1

To find the slope and the equation representing Francis's hike up Killington Hill, we can use the two points given in the problem. The points are:

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

Step 1: Calculate the slope (m)

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in our points:

\[ m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65 \]

Step 2: Use the slope-point form of the line

We can use the slope-point form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Using the point (1, 100) and the slope we found (65):

\[ y - 100 = 65(x - 1) \]

Conclusion

The slope is 65, and the equation that represents the scenario is:

\[ y - 100 = 65(x - 1) \]

Thus, the correct response is:

65; y−100=65(x−1)