Question

y
28
24
20
16
12
8
4
new memberships
10 20 30 40 50 60 70
first-time customers
the equation of the line of best fit is y = 0.171x + 2.241.
could this line of best fit be used to make reasonable predictions?

Explanation:

Step1: Analyze Data Point Distribution

Check how close the red data points are to the line of best fit. The points lie relatively near the line, showing a strong linear trend (positive correlation) between first - time customers (x) and new memberships (y).

Step2: Evaluate Line of Best Fit Usefulness

A line of best fit is useful for prediction when data points have a clear linear relationship (clustered around the line). Since the points here are close to the line \(y = 0.171x+2.241\), the linear association is strong enough for reasonable predictions within the data's context (or for extrapolation if assumptions hold).

Answer:

Yes, the line of best fit can be used to make reasonable predictions because the data points show a strong linear association (they cluster closely around the line), indicating a consistent relationship between first - time customers and new memberships that the line models well.