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One spring day, Genesis noted the time of day and the temperature, in degrees Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 50° F. For the next 4 hours, the temperature rose 2° per hour. For the next 2 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 55° at midnight. On the set of axes below, graph Genesis's data.

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To graph Genesis's temperature data, we will break the information down into specific time intervals and temperatures. Below are the steps for plotting the data along a timeline:

  1. Starting Point:

    • Time: 6 a.m.
    • Temperature: 50° F

  2. First Interval (6 a.m. to 10 a.m.):

    • For the next 4 hours (from 6 a.m. to 10 a.m.), the temperature rises by 2° per hour:
      • 6 a.m.: 50° F
      • 7 a.m.: 52° F
      • 8 a.m.: 54° F
      • 9 a.m.: 56° F
      • 10 a.m.: 58° F

  3. Second Interval (10 a.m. to 12 p.m.):

    • For the next 2 hours (from 10 a.m. to 12 p.m.), the temperature rises by 3° per hour:
      • 11 a.m.: 61° F
      • 12 p.m.: 64° F

  4. Steady Interval (12 p.m. to 6 p.m.):

    • From 12 p.m. to 6 p.m. (6 hours) the temperature remains steady at 64° F.

  5. Third Interval (6 p.m. to 10 p.m.):

    • For the next 4 hours (from 6 p.m. to 10 p.m.), the temperature drops by 2° per hour:
      • 7 p.m.: 62° F
      • 8 p.m.: 60° F
      • 9 p.m.: 58° F
      • 10 p.m.: 56° F

  6. Fourth Interval (10 p.m. to 12 a.m.):

    • The temperature continues to drop until it reaches 55° F by midnight. From 10 p.m. to midnight (2 hours), the temperature drops from 56° F to 55° F, which is a drop of 1° per hour:
      • 11 p.m.: 55° F
      • 12 a.m.: 55° F

Summary of Temperature Data Points:

| Time | Temperature (°F) | |----------|-------------------| | 6 a.m. | 50 | | 7 a.m. | 52 | | 8 a.m. | 54 | | 9 a.m. | 56 | | 10 a.m. | 58 | | 11 a.m. | 61 | | 12 p.m. | 64 | | 1 p.m. | 64 | | 2 p.m. | 64 | | 3 p.m. | 64 | | 4 p.m. | 64 | | 5 p.m. | 64 | | 6 p.m. | 64 | | 7 p.m. | 62 | | 8 p.m. | 60 | | 9 p.m. | 58 | | 10 p.m. | 56 | | 11 p.m. | 55 | | 12 a.m. | 55 |

Graphing Instructions:

  1. Draw the axes, labeling the x-axis with the time from 6 a.m. to 12 a.m. (midnight) and the y-axis with the temperature in degrees Fahrenheit.
  2. Plot each of the points listed in the table above.
  3. Connect the points according to the temperature changes in each time interval, ensuring to use straight lines for constant temperature periods and gradual slopes for increasing or decreasing temperature.
  4. Ensure to label important points and intervals on the graph for clarity.

Feel free to utilize graphing software or manual graph paper to visualize this data!