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 average number of posts per friend
y is equal to 0 point 0 0 4 x minus 4; the slope represents the average number of posts per friend
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 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=0.5x−4
; the slope represents the amount of increase in the GPA for each post
The linear function that best models the line of best fit is y=0.004x−4. The slope in this equation represents the average number of posts per friend.
To determine the linear function that best models the line of best fit on the scatter plot, we need to analyze the provided options. The correct linear function is the one where the slope represents the relationship between the number of posts and the GPA.
Let's evaluate the options:
1. y=0.004x−4
This option states that the slope represents the average number of posts per friend. However, we are interested in the relationship between posts and GPA, not the average number of posts.
2. y=−0.004x+4
This option states that the slope represents the amount of decrease in the GPA for each post. This does not align with our goal of determining the relationship between posts and GPA.
3. y=−0.5x−4
Here, the slope represents the amount of decrease in GPA for each post. This option is similar to the previous one and does not match our objective.
4. y=0.5x−4
This option states that the slope represents the amount of increase in the GPA for each post. This aligns with our goal of determining the relationship between posts and GPA.
Therefore, the linear function that best models the line of best fit is:
y = 0.5x - 4
In this equation, the slope represents the amount of increase in GPA for each post.
To determine which linear function best models the line of best fit, we need to understand what the slope in the equation represents.
The slope of a linear function represents the rate of change between two variables. In this case, the slope will represent the relationship between the number of times friends post on social media and their grade point averages (GPA).
Let's examine the given options:
1) y=0.004x−4: This option suggests that the slope is 0.004. Therefore, for each increase of 1 in the number of posts, the GPA would increase by 0.004. However, it seems unlikely that posting on social media would have such a small impact on GPA.
2) y=−0.004x+4: In this option, the slope is -0.004. This implies that for every post on social media, the GPA decreases by 0.004. This could be a possible relationship, suggesting that more posts result in a lower GPA.
3) y=−0.5x−4: The slope in this option is -0.5, meaning that for every post on social media, the GPA decreases by 0.5. This suggests a stronger negative relationship between posting frequency and GPA compared to the previous option.
4) y=0.5x−4: In this case, the slope is 0.5, indicating that for each post on social media, the GPA increases by 0.5. This suggests a positive relationship between posting frequency and GPA.
Based on the given options, the linear function that best models the line of best fit would be option 3: y=−0.5x−4. This option has a slope of -0.5, representing the amount of decrease in GPA for each post on social media.