Question

In Alaska, the temperature outside when you wake up is -4 degrees. The temperature increases by 1 degree for every hour over the next 10 hours. Which of the following graphs best models this temperature? (1 point)

Answer 1

To model the temperature changes over time in Alaska starting from -4 degrees and increasing by 1 degree each hour for 10 hours, we can express the temperature \( T \) as a function of time \( t \) in hours.

The temperature at time \( t \) is given by:

\[
T(t) = -4 + t
\]

where \( t \) ranges from 0 to 10 (representing the hours after waking up).

### Key Points to Consider for the Graph:

- At **\( t = 0 \)** (when you wake up), the temperature is **-4 degrees**.
- At **\( t = 1 \)**, the temperature will be **-3 degrees**.
- At **\( t = 2 \)**, the temperature will be **-2 degrees**.
- ...
- At **\( t = 10 \)**, the temperature will be **6 degrees**.

### Characteristics of the Graph:

1. **Linear Increase**: The graph will be a straight line because the temperature increases at a constant rate (1 degree per hour).
2. **Starting Point**: The line will start at the point (0, -4).
3. **Ending Point**: The line will end at the point (10, 6).
4. **Slope**: The slope of the line is 1, indicating that for every hour (increase in t), the temperature increases by 1 degree (increase in T).

Based on these characteristics, you should look for a straight line graph that starts at -4 on the y-axis when \( t = 0 \) and rises to 6 when \( t = 10 \). The line should have a steady upward slope, showing consistent increase over the 10 hours.

Select the graph that matches these conditions.