1. **State the problem:** Interpret the linear function from the graph and table related to volunteers cleaning trails. 2. **Part a:** What does the ordered pair (1, 1000) represent? - It means after 1 hour of work, the elevation reached is 1000 feet. 3. **Part b:** The graph starts at 720 on the y-axis. - This is the initial elevation before any work started, so it is the initial value, not the rate of change. 4. **Part c:** Find the elevation increase per hour (rate of change). - From (1, 1000) and (0, 720), rate of change $m = \frac{1000 - 720}{1 - 0} = \frac{280}{1} = 280$ feet per hour. - This is the rate of change. 5. **Part d:** Write the equation of the function. - Using point-slope form: $y = mx + b$ - $m = 280$, $b = 720$ - So, $$y = 280x + 720$$ 6. **Second problem:** Table of people vs time. - Points: (1, 150), (3, 250), (5, 350) 7. Calculate rate of change: - $m = \frac{250 - 150}{3 - 1} = \frac{100}{2} = 50$ 8. Find initial value $b$ using point (1, 150): - $150 = 50(1) + b \Rightarrow b = 150 - 50 = 100$ 9. Equation: - $$y = 50x + 100$$ 10. Interpretation: - Initial value 100 could represent 100 people at time 0. - Rate of change 50 means 50 more people arrive each hour. Final answers: - Elevation function: $$y = 280x + 720$$ - People function: $$y = 50x + 100$$