The question asks for the expected change in temperature if the time increases by 5 hours, based on the trend line equation shown in the scatter plot.

The equation of the trend line is:

$y = 1.85x + 0.04$

Where:

• $y$ is the temperature change (in °C),
• $x$ is the time (in hours).

To find the expected change in temperature after an increase of 5 hours, we need to calculate how much the temperature will increase based on the slope of the trend line.

Key Insight:

The slope of the trend line ($1.85$) represents the rate of change in temperature per hour. Therefore, for every hour, the temperature increases by $1.85^\circ C$.

For 5 hours:

$\text{Temperature change} = 1.85 \times 5 = 9.25^\circ C$

This is closest to "The temperature will increase by approximately 10°C."

Final Answer:

The correct option is "The temperature will increase by approximately 10°C."

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the slope of a line affect predictions in linear regression?
2. What would happen if the slope of the trend line was negative?
3. How would the prediction change if you were asked about a 2-hour increase instead?
4. Can the intercept value ($0.04$) affect the rate of change in the temperature?
5. What are other real-world examples of interpreting trend lines?

Tip: The slope in a trend line tells you the rate of change, which helps predict values even outside the given data range.