Question

number of social media posts vs. gpa
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?

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \) (social media posts = 0), \( y = 4 \) (GPA = 4). Another point: when \( x = 400 \), \( y = 0.5 \)? Wait, no, looking at the y - axis, the intercept is at (0, 4) and let's take another point. Let's take (0, 4) and (400, 0.5)? Wait, maybe better to take (0, 4) and (200, 2.5)? Wait, no, let's check the grid. The line starts at (0, 4) and goes down. Let's use (0, 4) and (400, 0.5) is not correct. Wait, maybe (0, 4) and (400, 0) but the line ends at y = 0.5? Wait, no, the y - axis has GPA from 0 to 4, x - axis social media posts from 0 to 400. Let's take two clear points: (0, 4) and (400, 0). Wait, the line of best fit: when x = 0, y = 4; when x = 400, y = 0. So the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{400 - 0}=\frac{- 4}{400}=-0.01 \). So the equation is \( y=-0.01x + 4 \).

Step2: Interpret the slope

The slope is - 0.01. In the context of the problem, x is the number of social media posts, y is GPA. So the slope represents the change in GPA per unit change in the number of social media posts. So for each additional social media post, the GPA decreases by 0.01 on average.

Answer:

The linear function is \( y=-0.01x + 4 \) (or similar with the correct slope). The slope represents the average decrease in GPA (by 0.01) for each additional social media post.