1. **State the problem:** We need to analyze Jack's temperature data throughout the day starting at 6 a.m. and graph the temperature changes. 2. **Given data:** - At 6 a.m., temperature = 50°F. - From 6 a.m. to 8 a.m. (2 hours), temperature rises 4°F per hour. - From 8 a.m. to 11 a.m. (3 hours), temperature rises 2°F per hour. - From 11 a.m. to 6 p.m. (7 hours), temperature stays steady. - From 6 p.m. to 8 p.m. (2 hours), temperature drops 1°F per hour. - From 8 p.m. to midnight (4 hours), temperature drops steadily to 59°F. 3. **Calculate temperature at key times:** - At 8 a.m.: $$50 + 2 \times 4 = 50 + 8 = 58$$ - At 11 a.m.: $$58 + 3 \times 2 = 58 + 6 = 64$$ - From 11 a.m. to 6 p.m., temperature stays at 64°F. - At 8 p.m.: $$64 - 2 \times 1 = 64 - 2 = 62$$ - From 8 p.m. to midnight, temperature drops from 62°F to 59°F over 4 hours. 4. **Find rate of temperature drop from 8 p.m. to midnight:** $$\text{Rate} = \frac{59 - 62}{4} = \frac{-3}{4} = -0.75 \text{°F per hour}$$ 5. **Summary of temperature at key times:** - 6 a.m.: 50°F - 8 a.m.: 58°F - 11 a.m.: 64°F - 6 p.m.: 64°F - 8 p.m.: 62°F - 12 a.m.: 59°F 6. **Graphing:** The temperature changes can be graphed as line segments connecting these points: - (6, 50) to (8, 58) - (8, 58) to (11, 64) - (11, 64) to (18, 64) - (18, 64) to (20, 62) - (20, 62) to (24, 59) This completes the analysis and plotting points for Jack's temperature data.