Question

Which two points should the line of best fit go through to best represent the data in the scatterplot?

A graph with points (1, 3), (2, 7), (3, 8), (4, 11), (5, 12), (6, 13).
(1, 3) and (2, 7)
(1, 3) and (6, 13)
(3, 8) and (5, 12)
(5, 12) and (6, 13)

Answer 1

To determine which two points the line of best fit should go through to best represent the data in the scatterplot, we should consider points that are well dispersed and cover the trend of the graph.

Looking at the given points:
- (1, 3)
- (2, 7)
- (3, 8)
- (4, 11)
- (5, 12)
- (6, 13)

The line of best fit should ideally capture the trend from the lower left to the upper right of the graph.

- **(1, 3) and (6, 13)**: These points represent the lower and upper extremes, showing the range of the data effectively.

- **(3, 8) and (5, 12)**: These points are closer together; while they do represent part of the data, they don't capture the trend as well as the extremes do.

- **(1, 3) and (2, 7)** or **(5, 12) and (6, 13)** would also not cover the full range effectively.

Therefore, the best choice would be **(1, 3) and (6, 13)** because these points provide a clear trend line that encompasses the entire dataset while indicating the positive correlation.