Question

Look at the data graphed on the scatter plot below.

A scatter plot is shown with data points showing a strong positive relationship. The x-values of the data points extend from 0 to 8, and the y-values of the data points extend from 1 to 6.
Which graph shows the line of best fit for the data?

A.
A scatter plot is shown with data points showing a strong positive relationship. The x-values of the data points extend from 0 to 8, and the y-values of the data points extend from 1 to 6.The line of best fit passes through the points (1.5, 2) and (5, 4.5)

B.
A scatter plot is shown with data points showing a strong positive relationship. The x-values of the data points extend from 0 to 8, and the y-values of the data points extend from 1 to 6.The line of best fit passes through the points (1, 1) and (1.5, 1.5).

C.
A scatter plot is shown with data points showing a strong positive relationship. The x-values of the data points extend from 0 to 8, and the y-values of the data points extend from 1 to 6.The line of best fit passes through the points (2, 1) and (4, 4).

D.
A scatter plot is shown with data points showing a strong positive relationship. The x-values of the data points extend from 0 to 8, and the y-values of the data points extend from 1 to 6.The line of best fit passes through the points (1.5, 3.2) and (2, 3.5).

Answer 1

D

Reason: A best-fit line for this cloud should have a moderate positive slope (~0.6) and pass through the middle of the points. Slopes:
- A: (1.5,2)→(5,4.5) slope ≈ 0.714 (intercept ≈ 0.93, too low)
- B: (1,1)→(1.5,1.5) slope = 1 but only fits a tiny local segment
- C: (2,1)→(4,4) slope = 1.5 (too steep)
- D: (1.5,3.2)→(2,3.5) slope = 0.6 with intercept ≈ 2.3, which best matches the central trend of the data.