Question 28

A line of best fit can be drawn through the points (0, 36) and (11, 74).

The points (0, 36) and (11, 74) represent a strong linear relationship in the scatterplot, making them suitable for establishing a line of best fit.

A) (0, 36) and (11, 74)

This option is correct as the points are widely spaced and demonstrate a clear upward trend, which is ideal for drawing a line of best fit. The significant vertical and horizontal distance between these points indicates they can effectively represent the overall trend of the data.

B) (1, 39) and (6, 60)

While these points do indicate a positive relationship, they are relatively close together compared to option A. This closeness can lead to a less accurate representation of the overall trend, making them less effective for establishing a line of best fit.

C) (5, 50) and (6, 60)

This pair of points is too close to each other and represents a very slight change in both x and y values. Such proximity limits their ability to depict the broader trend in the scatterplot, which is essential for drawing an effective line of best fit.

D) (6, 60) and (8, 60)

These points are horizontally aligned, indicating no change in the y-value. This horizontal arrangement does not allow for a slope to be established, rendering them ineffective for drawing a line of best fit in a scatterplot context.

E) (8, 60) and (11, 74)

Although these points show an upward trend, they are not as effective as option A. The distance between these two points is smaller compared to (0, 36) and (11, 74), which reduces their ability to represent the overall data trend adequately.

Conclusion

The points (0, 36) and (11, 74) provide both a significant distance and a clear upward trend, making them the best choice for establishing a line of best fit. In contrast, the other options either lack sufficient distance, show minimal change, or do not exhibit a proper slope, thereby failing to accurately represent the data trend.