Question

The table below displays the outdoor temperature, in degrees Fahrenheit, at Alicia's house over several hours.

Hours Passed Temperature
0 63
1 66
2 69
3 72
4 75

Which equation best represents the temperature, T, at Alicia's house, after h hours have passed?
T = -3h + 63
T = 3h + 63
T = 4h + 63
T = 12h + 63

Answer 1

To find the equation that represents the temperature \( T \) at Alicia's house after \( h \) hours, we need to observe the relationship between the hours passed and the temperature.

From the table:

- At hour 0, the temperature is 63°F.
- At hour 1, the temperature is 66°F.
- At hour 2, the temperature is 69°F.
- At hour 3, the temperature is 72°F.
- At hour 4, the temperature is 75°F.

From the data, we can see that the temperature increases by 3°F for each hour that passes:

- From 63°F to 66°F (increase of 3°F over 1 hour)
- From 66°F to 69°F (increase of 3°F over 1 hour)
- From 69°F to 72°F (increase of 3°F over 1 hour)
- From 72°F to 75°F (increase of 3°F over 1 hour)

This indicates that the temperature increases linearly with time, specifically, it increases by 3 degrees for every hour.

We can express this relationship mathematically as:

\[
T = \text{initial temperature} + (\text{change per hour}) \times h
\]

In this case, the initial temperature is 63°F, and the change per hour is 3°F. Thus, the temperature after \( h \) hours can be written as:

\[
T = 3h + 63
\]

So, the equation that best represents the temperature \( T \) at Alicia's house after \( h \) hours is:

**T = 3h + 63**