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Brent is trying to figure out the relationship between the number of times his friends post on social media and their grade point averages (GPA). He records the collected data on a scatter plot. Which of the linear functions best models the line of best fit? What does the slope in the equation represent? (1 point) Responses y=−0.004x+4 ; the slope represents the amount of decrease in the GPA for each post y is equal to negative 0 point 0 0 4 x plus 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 is equal to 0 point 5 x minus 4; the slope represents the amount of increase in the GPA for each post y=−0.5x−4 ; the slope represents the amount of decrease in the GPA for each post y is equal to negative 0 point 5 x minus 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

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To determine which linear function best models the line of best fit for the relationship between the number of social media posts (x) and GPA (y), we need to consider the context of the problem.

Given that we're looking for the relationship between social media posting frequency and GPA, a negative slope would typically indicate that as the number of posts increases, the GPA tends to decrease, which might reflect a trend where increased social media activity correlates with lower academic performance.

Among the options provided, the functions with negative slopes are:

  1. \( y = -0.004x + 4 \); the slope represents the amount of decrease in the GPA for each post.
  2. \( y = -0.5x - 4 \); the slope represents the amount of decrease in the GPA for each post.
  3. \( y = -0.5x - 4 \); the slope represents the amount of decrease in the GPA for each post.

Of these, the first equation \( y = -0.004x + 4 \) indicates a very small change in GPA with each additional post (specifically, a decrease of 0.004 in GPA for each post), while \( y = -0.5x - 4 \) indicates a significant decrease of 0.5 in GPA for each post.

The choice that best matches a reasonable model, considering a more substantial effect, would likely be \( y = -0.5x - 4 \).

In conclusion:

  • The best fitting function is likely \( y = -0.5x - 4 \).
  • The slope represents the amount of decrease in the GPA for each post, specifically 0.5 GPA points for each additional post made on social media.