1. Problem 6: Find the slope of the line passing through points (7, -2) and (3, -2). The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (7, -2)$ and $(x_2, y_2) = (3, -2)$. 2. Calculate the slope: $$m=\frac{-2 - (-2)}{3 - 7} = \frac{-2 + 2}{3 - 7} = \frac{0}{-4} = 0$$ Since the numerator is zero, the slope is zero, meaning the line is horizontal. --- 3. Problem 7: Find the rate of change in the first 30 minutes after takeoff using points (0, 0) and (0.5, 24) (since 30 minutes = 0.5 hours). Using the slope formula: $$m=\frac{24 - 0}{0.5 - 0} = \frac{24}{0.5} = 48$$ The rate of change is 48 thousand feet per hour. --- 4. Problem 8: Find the rate of change from 1.5 hours to 3 hours using points (1.5, 36) and (3, 36). Calculate slope: $$m=\frac{36 - 36}{3 - 1.5} = \frac{0}{1.5} = 0$$ The rate of change is 0 thousand feet per hour, meaning altitude is constant during this time. Final answers: - Problem 6 slope: $0$ - Problem 7 rate of change: $48$ - Problem 8 rate of change: $0$