One spring day, Nathan noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 52° F. For the next 2 hours, the temperature rose 1° per hour. For the next 5 hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 56° at midnight. On the set of axes below, graph Nathan's data.
Since we are graphing the time of day and temperature, we will use the horizontal axis for time and the vertical axis for temperature.
First, we will graph the initial temperature of 52°F at 6 a.m..
Next, we will graph the temperature increase by 1°F per hour for the next 2 hours. This means that at 8 a.m., the temperature will be 52°F + 1°F + 1°F = 54°F.
Then, we will graph the temperature increase by 2°F per hour for the next 5 hours. Starting from 8 a.m., the temperature will increase by 2°F per hour for the next 5 hours. So at 1 p.m., the temperature will be 54°F + 2°F + 2°F + 2°F + 2°F + 2°F = 64°F.
The temperature then remains steady until 6 p.m., so we draw a horizontal line on the graph from 1 p.m. to 6 p.m. at a temperature of 64°F.
From 6 p.m. to 10 p.m., the temperature drops by 1°F per hour. So at 10 p.m., the temperature will be 64°F - 1°F - 1°F - 1°F - 1°F = 60°F. We then connect the points from 6 p.m. to 10 p.m. with a downward sloping line.
From 10 p.m. to midnight, the temperature drops steadily until it reaches 56°F. We connect the points from 10 p.m. to midnight with another downward sloping line.
The final graph should show a line that starts at 6 a.m. with a temperature of 52°F, increases to 54°F at 8 a.m., increases to 64°F at 1 p.m., remains steady until 6 p.m. at 64°F, drops to 60°F at 10 p.m, and finally drops to 56°F at midnight.
Please note that since we don't have any specific times for the temperature changes within each hour, we can only estimate the positions of the points on the graph.