Subjects algebra

Sky Diver Altitude Def564

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1. **Problem Statement:** Interpret the slope and y-intercept of the Sky Diver's Altitude graph, which shows altitude decreasing from 4000 ft at 0 min to 0 ft at 4 min. 2. **Formula for slope:** $$\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate slope:** Points: $(0,4000)$ and $(4,0)$ $$\text{slope} = \frac{0 - 4000}{4 - 0} = \frac{-4000}{4} = -1000$$ 4. **Interpret slope units:** Since $y$ is altitude in feet and $x$ is time in minutes, slope units are feet per minute (ft/min). 5. **Interpret slope meaning:** The slope is $-1000$ ft/min, meaning the skydiver loses 1000 feet of altitude every minute. 6. **Identify y-intercept:** The y-intercept is the altitude at time 0, which is $(0,4000)$. 7. **Interpret y-intercept meaning:** At time 0 minutes, the skydiver is at 4000 feet altitude. 8. **Summary statements:** - Slope: For every 1 minute, the altitude decreases by 1000 feet. - Y-intercept: At 0 minutes, the altitude is 4000 feet. Final answers: - Slope: $-1000$ feet/min - Y-intercept: $(0,4000)$