1. The problem states that Francis is hiking up Killington Hill and we know two points on his elevation path: after 1 hour, elevation is 100 feet, and after 5 hours, elevation is 360 feet. 2. We need to find the slope $m$ of the line connecting these two points and then write the equation of the line representing elevation $y$ as a function of time $x$. 3. The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (1, 100)$ and $(x_2, y_2) = (5, 360)$. 4. Calculate the slope: $$m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65$$ 5. Use point-slope form of a line equation: $$y - y_1 = m(x - x_1)$$ Substitute $m=65$ and point $(1, 100)$: $$y - 100 = 65(x - 1)$$ 6. This equation models Francis's elevation over time. Final answer: Slope $m = 65$ Equation: $y - 100 = 65(x - 1)$