Question

which two points should the line of best fit go through to best represent the data in the scatterplot?
(1,16) and (2,15)
(1,16) and (6,1)
(2,15) and (4,9)
(5,8) and (6,1)

Explanation:

Step1: Understand the concept of line of best fit

The line of best fit should pass through points that represent the overall trend of the data. It should balance the points above and below the line.

Step2: Analyze each option

• Option (1, 16) and (2, 15): These two points are close to each other and do not capture the full range of the data's trend.
• Option (1, 16) and (6, 1): These two points span the entire range of \(x\) - values (\(x = 1\) to \(x=6\)) and also represent the decreasing trend of the data (as \(x\) increases from \(1\) to \(6\), \(y\) decreases from \(16\) to \(1\)).
• Option (2, 15) and (4, 9): These points do not cover the left - most (\(x = 1\)) and right - most (\(x = 6\)) data points well.
• Option (5, 8) and (6, 1): These points only cover a small part of the \(x\) - range (\(x = 5\) to \(x = 6\)) and do not represent the data from \(x=1\) to \(x = 4\) effectively.

Answer:

\((1,16)\) and \((6,1)\)