Luis created the graph below to show the temperature
from 8:00 a.m. (8 hours after midnight) until 8:00 pm
Which statements are true about the temperatures Luis
recorded on the graph? Check all that apply.
Hourly Temperature
The temperature increased until 4:00 p.m.
12%
The temperature was not recorded between 4:00 pm
and 6:00 pm
Temperature (°F)
The temperature decreased after 6:00 pm
The temperature increased and then decreased before
holding constant
1
2
4
6
8
10 12 14 16
18 20
w T
The temperature increased more quickly between 12:00
pm and 4:00 pm than before 12:00 pm
op

The relationship between temperature and time as seen on the attached graph is a nonlinear relationship. This means that the rates on the graph will increase, decrease and also be at constant at different points on the graph.

The correct options (i.e. true statements) from the graph are:

The temperature increased until 4:00 p.m.

The temperature decreased after 6:00 pm

The temperature increased more quickly between 12:00 pm and 4:00 pm than before 12:00 pm

Please see attachment for missing graph.

The time (in 24-hour format) were plotted on the x-axis while the temperature were plotted on the y-axis. So, we have:

[tex](x,y) \to (time,temperature)[/tex]

Option (a)

Notice that there is a straight line from (12,0) to (16,8).

The temperature change is:

[tex]y = 8 - 0 = 8[/tex]

When the time is represented as 12-hour format, it means that the temperature increased by [tex]8^oF[/tex] from 12:00pm to 04:00pm.

Hence, (a) is true.

Option (b)

The temperature between 4:00pm and 6:00pm is represented with the straight horizontal line from (16,8) to (18,8).

The temperature between this interval is uniform at [tex]8^oF[/tex].

Hence, (b) is false.

Option (c)

The temperature at 6pm is represented as: (18,8).

Notice that the line from (18,8) moves towards the x-axis. This means that the temperature reduced after 6:00pm.

Hence, (c) is true

Option (d)

At no point on the attached graph, did the line of the graph shows an increment immediately followed by a decrement.

Hence, (d) is false.

Option (e)

The straight line from (8,-4) to (12,0) shows that the temperature increased till 12:00pm

The rate of this line is:

[tex]m = \frac{0 --4}{12 - 8} = \frac{4}{4} = 1[/tex]

The straight line from (12,0) to (16,8) shows that the temperature also increased from 12:00pm to 4:00pm

The rate of this line is:

[tex]m = \frac{8 -0}{16 - 12} = \frac{8}{4} = 2[/tex]

Because 2 > 1, the line from (12,0) to (16,8) has a higher rate than the line from (8,-4) to (12,0).

This means temperature increased more between 12:00 and 4:00pm

Hence, (e) is true.