To find the slope of the line of best fit for the given data, we need to follow these steps:
1. Extract the Data: First, list the latitudes and the corresponding high temperatures.
- Latitudes ([tex]\(N^\circ\)[/tex]): 42, 45, 39, 35, 32, 41, 40, 33, 30
- High Temperatures ([tex]\(^{\circ} F\)[/tex]): 53, 41, 67, 63, 70, 58, 61, 67, 72
2. Understand the Relationship: We assume a linear relationship between the variables, latitude and temperature. The line of best fit seeks to best represent this relationship.
3. Calculate the Line of Best Fit: Using methods such as linear regression, the line of best fit can be calculated. The form of this linear equation is:
[tex]\[
\text{Temperature} = m \cdot \text{Latitude} + b
\][/tex]
where [tex]\(m\)[/tex] is the slope of the line.
4. Interpret the Slope: The slope [tex]\(m\)[/tex] tells us the change in temperature for each one degree increase in latitude. A negative slope implies that temperature decreases as latitude increases, and vice versa.
5. Slope Calculation Result: After calculating the slope of the line of best fit for the provided data, we find that the slope is approximately [tex]\(-1.671\)[/tex].
6. Rounding the Slope: We round the slope to one decimal place, resulting in [tex]\(-1.7\)[/tex].
7. Choose the Correct Statement:
- A slope of [tex]\(-1.7\)[/tex] means the temperature decreases by approximately [tex]\(1.7^{\circ} F\)[/tex] for each 1 degree increase north in latitude.
Therefore, the statement that best describes the slope of the line of best fit for the data is:
- "The temperature decreases by about [tex]\(1.7^{\circ}\)[/tex] for each 1 degree increase north in latitude."
