Question

Which two points would a line of fit go through to best fit the data?

(3, 7) and (9, 1)
(1, 8) and (8, 1)
(1, 9) and (5, 7)
(1, 7) and (2, 5)

Answer 1

To determine which two points would make the best line of fit, we want to consider the overall trend of the points and how they relate to each other. Generally, we should look for points that would create a line that best represents the overall trend of a potential set of data points.

Here's a brief analysis of each pair:

1. **(3, 7) and (9, 1)**: This line would have a negative slope, indicating a decrease from the first point to the second.

2. **(1, 8) and (8, 1)**: This would also create a negative slope, but it spans a wider range on the x-axis (from 1 to 8), suggesting a steeper decline.

3. **(1, 9) and (5, 7)**: This line would have a gentle negative slope, indicating a slight decrease.

4. **(1, 7) and (2, 5)**: This would also create a negative slope, but it’s a very short span and would resemble a gentle decline.

To determine the best fit, we should consider which pair spans a wider range while also maintaining a representative trend of decline (if that is the overall direction suggested by context), as this will give a more accurate representation of variability.

If we assume the data is showing a trend downwards, either the first pair **(3, 7) and (9, 1)** or the second pair **(1, 8) and (8, 1)** would produce a more noticeable negative slope.

Based on the analysis, the pair **(1, 8) and (8, 1)** would likely create a better line of fit due to their broader range and clear downward trend.

Therefore, the answer is: **(1, 8) and (8, 1)**.