First, let's understand the context of the problem. We have a table showing the latitudes and corresponding high temperatures on the first day of spring for various locations with the same longitude.
To summarize the question: we are given pairs of data points (latitude, temperature) and asked to determine the slope of the line of best fit for this data set. The slope will tell us how the temperature changes with increasing latitude.
We can proceed with these steps to calculate and interpret the slope:
1. Organize the Data:
- Latitudes: [tex]\([42, 45, 39, 35, 32, 41, 40, 33, 30]\)[/tex]
- Temperatures: [tex]\([53, 41, 67, 63, 70, 58, 61, 67, 72]\)[/tex]
2. Fit a Line to the Data:
- In statistical and mathematical analysis, one common approach to determine the relationship between two variables is by fitting a line, often referred to as the "line of best fit" or "regression line".
3. Determine the Slope:
- The slope of this line of best fit indicates how much the temperature changes for each one-degree change in latitude.
- Through linear regression analysis, the slope has been calculated.
4. Interpret the Slope:
- Given the numerical data analysis, the slope is found to be approximately -1.7.
5. Conclusion:
- A negative slope indicates that as latitude increases (moving northward), the temperature decreases.
- Specifically, for each 1-degree increase in latitude, the temperature decreases by about 1.7 degrees.
Therefore, the correct statement is:
"The temperature decreases by about [tex]\(1.7^{\circ}\)[/tex] for each 1 degree increase north in latitude."
