Question

abby wants to understand how hanging out with friends impacts her social media usage. over a couple of months, she recorded the hours per week she spent doing each activity. then, she made a scatter plot. the x-axis shows the number of hours spent with friends, and the y-axis shows the number of hours spent on social media. the scatter plot also shows a line of best fit. the equation for the line of best fit is $y = -\frac{4}{5}x + 4$. in this context, what can you conclude from the y-intercept? for every 5 hours abby spends with friends, she spends about 4 hours on social media. for every 4 hours abby spends with friends, she spends about 5 hours on social media. if abby spends no time on social media, she can expect to spend about 4 hours with friends. if abby spends no time with friends, she can expect to spend about 4 hours on social media.

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a line \(y = mx + b\) is \(b\), occurring when \(x = 0\).

Step2: Apply to the context

Here, \(x\) = hours with friends, \(y\) = hours on social media. When \(x = 0\) (no time with friends), \(y = -\frac{4}{5}(0) + 4 = 4\). This means Abby spends ~4 hours on social media when she spends 0 hours with friends.

Answer:

If Abby spends no time with friends, she can expect to spend about 4 hours on social media.