Brent is trying to figure out the relationship between the number of times his friends post on social media and their grade point averages. 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?
a
y = 0.004x - 4; the average number of posts per friend
b
y = 0.05x - 4; the amount of increase in the GPA for each post
c
y = -0.004x + 4; the amount of decrease in the GPA for each post
d
y = -0.5x - 4; the amount of decrease in the GPA for each post
It is impossible to determine which linear function best models the line of best fit without knowing the actual data plotted on the scatter plot. The slope in the equation represents the rate of change in the dependent variable (in this case, the GPA) for each unit increase in the independent variable (the number of posts).
educated guess
Without knowing the actual data plotted on the scatter plot, it is still difficult to make an educated guess for the linear function that best models the line of best fit. However, it is important to note that a positive slope indicates a positive correlation between the number of posts and the GPA, which would mean that as students post more on social media, their GPAs tend to increase. On the other hand, a negative slope would indicate a negative correlation, meaning that as students post more on social media, their GPAs tend to decrease.
To determine which linear function best models the line of best fit, we need to understand the relationship between the number of social media posts and the grade point averages (GPAs).
First, let's look at the slope in each equation and what it represents:
a) y = 0.004x - 4
In this equation, the slope is 0.004. The slope represents the amount of increase or decrease in the dependent variable (y) for each unit increase in the independent variable (x). Therefore, in this case, for each additional post, the GPA is expected to increase by 0.004.
b) y = 0.05x - 4
In this equation, the slope is 0.05. Similarly, it represents the amount of increase or decrease in the GPA for each post. Therefore, for each additional post, the GPA is expected to increase by 0.05.
c) y = -0.004x + 4
Here, the slope is -0.004. The negative slope suggests that for each additional post, the GPA is expected to decrease by 0.004.
d) y = -0.5x - 4
In this equation, the slope is -0.5. Similarly, it represents the amount of decrease in the GPA for each post. Therefore, for each additional post, the GPA is expected to decrease by 0.5.
Considering the context of Brent's investigation, it seems more logical that the number of posts on social media would have a positive impact on GPAs rather than a negative one. Therefore, option b (y = 0.05x - 4; the amount of increase in the GPA for each post) best represents the relationship between the number of times Brent's friends post on social media and their grade point averages.