Final answer:
In discussing an application problem, the practical values of the independent variable are context-specific, such as state rankings explaining area differences. Visual tools like scatter plots and the least-squares regression line, alongside interpreting the y-intercept and slope, reveal relationships and data trends.
Step-by-step explanation:
When analyzing an application problem in mathematics, the values of the independent variable that have a practical interpretation are those that align with the context of the problem. For instance, if we are studying the relationship between the ranking of a state and the area of the state, the independent variable would typically be the ranking, as this is the variable that we believe will explain changes in the dependent variable, which is the area.
To find these relationships, we would first construct a scatter plot to visualize the data. Then, we'd use a calculator's regression function to find the least-squares regression line. This line helps us understand the relationship between the independent and dependent variables, often revealing if there’s a linear relationship and how strong it is, indicated by the correlation coefficient. In this context, the y-intercept represents the predicted area when the ranking is zero, and the slope represents the change in the predicted area for each unit increase in ranking.
When interpreting the functionality of an equation within an application problem, consider the variables involved. For example, in an economic context, one may consider how different factors affect the GPA implying the GPA is the dependent variable altered by various independent variables like study hours, class attendance, etc.