Question

while spending time with his extended family, doug asked his family members for their ages, x, and how many books they had read in the past year, y. then, he created a scatter plot and drew a line of best fit. the equation for the line of best fit is $y = -\frac{1}{3}x + 22$. in this context, what does the slope tell you? getting 3 years older was associated with reading 1 less book per year. getting 1 year older was associated with reading 3 fewer books per year. dougs family members tended to read fewer than 22 books. dougs family members tended to read at least 22 books.

Explanation:

The line of best fit is in slope-intercept form \(y = mx + b\), where \(m\) (slope) is \(-\frac{1}{3}\). This means for each 1-year increase in age (\(x\)), the number of books read (\(y\)) decreases by \(\frac{1}{3}\). Scaling up, a 3-year age increase (\(3 \times 1\)) leads to a \(3 \times \frac{1}{3} = 1\) book decrease, matching the first option. Other options misinterpret the slope or y-intercept.

Answer:

Getting 3 years older was associated with reading 1 less book per year.