1. Ernest calculated the slope of the graph during the uphill climb to be 10. His work is shown below. Determine whether his calculation was correct or incorrect, and then explain why. (2 points: 1 for the answer, 1 for the explanation)

Points: (60,900) (15,450)
Slope: 900-450/60-15 = 450/45 = 10

2. Confirm or disprove Ernest's work by selecting two different points and applying the slope formula. Be sure to identify the points you chose. (2 points)

3. What does the slope tell you about the rate of change in elevation during Ryan's uphill climb? What was the total elevation change? (2 points: 1 for identifying the rate of change, 1 for the total elevation change)

4. What is the slope of the graph between 120 and 150 minutes? What does this mean in terms of change in elevation? (2 points: 1 for the slope, 1 for the explanation)

5. Ernest thinks that Ryan rested between 120 and 150 minutes. Emma thinks he walked on a flat part of the trail during that time. Whose hypothesis is valid: Ernest's, Emma's, or both? Write a detailed explanation of whether each hypothesis is an acceptable interpretation of the graph. (4 points)

Ernest's hypothesis (resting between 120 and 150 minutes):

Emma's hypothesis (walking on a flat trail between 120 and 150 minutes):

6. Emma calculated the slope of the downhill hike to be -1/40 . Her work is shown below. Determine whether her calculation was correct or incorrect, and then explain why. (2 points: 1 for the answer, 1 for the explanation)

Points: (165,900), (180,300)
Slope: 180-165/300-900 = 15/-600 = -1/40

7. Confirm or disprove Emma's work by using two other points from the slope of the downhill hike. (1 point)

8. What does the slope tell you about the rate of change in elevation during descent? (1 point for identifying the rate of change)

9. It took Ryan less time to hike down than it did to hike up. Ernest thinks that was because Ryan jogged down the same trail he went up. Emma thinks the trail down was steeper than the trail up. Whose hypothesis is valid: Ernest's, Emma's, or both? Write a detailed explanation of whether each hypothesis is an acceptable interpretation of the graph. (4 points)

Ernest's hypothesis (jogged down same trail):

Emma's hypothesis (steeper trail):