To determine the best linear function that models the relationship between the number of times Brent's friends post on social media and their GPA, we need to consider the general form of a linear equation, which is \(y = mx + b\). Here, \(m\) represents the slope and \(b\) is the y-intercept.
Since the context suggests that increased posting might lead to a decrease in GPA (which is a common assumption), we would expect the slope \(m\) to be negative.
Looking at the responses:
- y = -0.5x - 4; the slope represents the amount of decrease in the GPA for each post.
- y = -0.004x + 4; the slope represents the amount of decrease 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 increase in the GPA for each post.
From these, the first two options have a negative slope, which aligns with our expectation. The other options indicate a positive slope, suggesting an increase in GPA with more social media posts, which is contrary to the assumption.
The most appropriate choice depends on the magnitude of the change in GPA with each post. Typically, a small decrease in GPA would be represented by a smaller slope value, such as -0.004. In contrast, -0.5 suggests a more significant impact.
If we assume a small negative impact on GPA, the best model may be:
y = -0.004x + 4; the slope represents the amount of decrease in the GPA for each post.
In this case, the slope (-0.004) indicates that for each additional post made by a friend, the GPA decreases by 0.004 points, which suggests that while there's an impact, it is relatively small.
However, if a more substantial impact is intended in a particular context, then:
y = -0.5x - 4; the slope represents the amount of decrease in the GPA for each post.
In summary, you'll need to determine the best fit based on the context of the data and the expected relationship.