Let's break this down step by step to graph Luis's data and understand the temperature changes over time.

Timeline Breakdown:

1. 6 a.m.: The temperature was $50^\circ F$.

2. 6 a.m. to 10 a.m. (4 hours): The temperature increased by $4^\circ F$ per hour.

   • By $10 \, \text{a.m.}$, the temperature increase was $4 \times 4 = 16^\circ F$.
   • So, the temperature at $10 \, \text{a.m.}$ was $50^\circ F + 16^\circ F = 66^\circ F$.

3. 10 a.m. to 1 p.m. (3 hours): The temperature rose $1^\circ F$ per hour.

   • By $1 \, \text{p.m.}$, the temperature increased $1 \times 3 = 3^\circ F$.
   • So, the temperature at $1 \, \text{p.m.}$ was $66^\circ F + 3^\circ F = 69^\circ F$.

4. 1 p.m. to 6 p.m. (5 hours): The temperature remained steady at $69^\circ F$.

5. 6 p.m. to 9 p.m. (3 hours): The temperature dropped $2^\circ F$ per hour.

   • By $9 \, \text{p.m.}$, the temperature decreased $2 \times 3 = 6^\circ F$.
   • So, the temperature at $9 \, \text{p.m.}$ was $69^\circ F - 6^\circ F = 63^\circ F$.

6. 9 p.m. to midnight (3 hours): The temperature dropped steadily until it reached $60^\circ F$.

   • At midnight, the temperature was $60^\circ F$.

Points to Plot:

• At $6 \, \text{a.m.}$: $(6, 50)$
• At $10 \, \text{a.m.}$: $(10, 66)$
• At $1 \, \text{p.m.}$: $(13, 69)$
• From $1 \, \text{p.m.}$ to $6 \, \text{p.m.}$: The temperature stays at $69$, so we have $(18, 69)$.
• At $9 \, \text{p.m.}$: $(21, 63)$
• At midnight: $(24, 60)$

Graphing Instructions:

• Plot time on the x-axis from 6 a.m. (6) to midnight (24).
• Plot temperature on the y-axis.
• Connect the points to form a continuous graph, reflecting the changes in temperature.

Would you like to see the graph plotted or need further clarifications?

Related Questions:

1. What would the temperature be if the temperature rose by 3° per hour after 1 p.m.?
2. How would the graph look if the temperature decreased by 1° per hour instead of 2° after 6 p.m.?
3. What is the average temperature throughout the day based on Luis’s data?
4. How would the graph change if the temperature stayed steady after 9 p.m.?
5. What would happen to the graph if the temperature started at 55°F instead of 50°F?

Tip:

Understanding how to represent real-world data as a graph helps improve your ability to model and interpret trends in various contexts.