To determine which linear function best models the line of best fit for the data collected by Brent, we need to understand what the slope represents in the context of the relationship between social media posts and GPA.
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If the slope is positive (like in the first or third options), it would imply that as the number of posts increases, the GPA also increases, which seems counterintuitive.
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If the slope is negative (like in the second or fourth options), it suggests that as the number of posts increases, the GPA decreases, which aligns with common concerns about social media affecting academic performance.
Considering these points, the second option:
y = -0.004x + 4; the slope represents the amount of decrease in the GPA for each post
indicates a small decrease in GPA as posts increase, which would likely be more realistic based on studies showing a negative correlation between social media usage and academic performance.
The fourth option:
y = -0.5x - 4; the slope represents the amount of decrease in the GPA for each post
indicates a steeper decline, which would also suggest a significant negative impact on GPA with increased social media activity.
Without specific data to analyze, it's hard to conclusively determine which model is the best fit, but the negative slope models (second and fourth options) align more closely with expected outcomes of GPA decrease with an increase in social media posts.
Thus, if I were to choose one based on general trends, I would select:
y = -0.004x + 4; the slope represents the amount of decrease in the GPA for each post
This indicates a small negative impact of social media posts on GPA, which is a reasonable assumption based on existing research.