To determine which linear function best models the line of best fit for Brent's data on social media posts and GPA, we need to consider two main aspects: the interpretation of the slope of the line and the nature of the relationship observed in the scatter plot.
The options presented include:
- y = −0.004x + 4; the slope represents the amount of decrease in the GPA for each post.
- y = 0.5x − 4; the slope represents the amount of increase in the GPA for each post.
- y = 0.004x − 4; the slope represents the average number of posts per friend.
- y = −0.5x − 4; the slope represents the amount of decrease in the GPA for each post.
If the relationship Brent is observing suggests that an increase in the number of social media posts leads to a decrease in GPA, the appropriate function would have a negative slope.
The first and fourth options show a decrease in GPA with negative slopes (-0.004 and -0.5 respectively), both of which indicate that with each additional post, the GPA decreases.
- The first option (y = −0.004x + 4) suggests a slight decrease in GPA per post (-0.004).
- The fourth option (y = −0.5x − 4) indicates a more significant decrease per post (-0.5).
Meanwhile, the second option suggests an increase in GPA (which contradicts the expected outcome if more posting correlates with lower GPAs), and the third option misinterprets the slope.
Thus, the two relevant functions to consider are the first and the fourth:
- If the negative slope is understood to represent the decline in GPA for each social media post, then the equation that best models the relationship (based on the assumption that increased posting correlates with lower GPAs) would be y = −0.5x − 4, with the slope (-0.5) indicating the amount of decrease in GPA for each post.
Therefore, the answer is: y = −0.5x − 4; the slope represents the amount of decrease in the GPA for each post.