1. **State the problem:** Francis is hiking up Killington Hill. After 1 hour, his elevation is 100 feet, and after 5 hours, it is 360 feet. We need to find the slope of the line representing his elevation over time and write the equation of that line. 2. **Formula for slope:** The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** Using points $(1, 100)$ and $(5, 360)$: $$m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65$$ 4. **Write the point-slope form equation:** The point-slope form is: $$y - y_1 = m(x - x_1)$$ Using point $(1, 100)$ and slope $65$: $$y - 100 = 65(x - 1)$$ 5. **Interpretation:** The slope $65$ means Francis gains 65 feet in elevation each hour. The equation $y - 100 = 65(x - 1)$ models his elevation $y$ at time $x$ hours. **Final answer:** Slope is $65$ and the equation is $$y - 100 = 65(x - 1)$$.