Question

the data show a correlation.
c. interpret the slope and the y -intercept of the line of best fit.

the slope, m , means the number of people who volunteer decreases by m each day. the y -intercept, b , indicates the number of people who who volunteer at the shelter the first day.

the slope, m , means the number of people who volunteer increases by m each day. the y -intercept, b , has no meaning because there is no day 0.

the slope, m , means the number of people who volunteer decreases by m each week. the y -intercept, b , means the number of people who volunteer at the shelter on the last day.

the slope, m , means the number of people who volunteer increases by m each day. the y -intercept, b , has no meaning in this context because the number of people cannot be 0.

Explanation:

To determine the correct interpretation, we analyze each option:

1. First option: If slope is negative (decrease), but the last option's reasoning about y - intercept (people can't be 0) is more context - appropriate. Also, the first option's y - intercept description (first day) is incorrect as y - intercept is at day 0.
2. Second option: "No day 0" is not a strong reason. Usually, in volunteer - day context, day 0 can be conceptual (e.g., before the first day of volunteering tracking), but the last option's reasoning about people number not being 0 is better.
3. Third option: Slope as decrease per week is inconsistent with the "day" - based context of other options, and y - intercept as last day is wrong.
4. Fourth option: Slope as increase per day makes sense for a positive trend (if applicable), and y - intercept (day 0) would imply 0 volunteers, which is impossible as you can't have 0 people if there is volunteering (or the context of tracking volunteers), so y - intercept has no meaning here.

Answer:

The slope, \( m \), means the number of people who volunteer increases by \( m \) each day. The \( y \) - intercept, \( b \), has no meaning in this context because the number of people cannot be 0.