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A scatter plot is shown on the coordinate plane.

scatter plot with points plotted at 1 comma 3, 2 comma 5, 3 comma 4, 3 comma 7, 4 comma 6, 5 comma 4, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 8, 9 comma 6, and 10 comma 8

Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 3, 2 comma 5, 3 comma 4, 3 comma 7, 4 comma 6, 5 comma 4, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 8, 9 comma 6, and 10 comma 8, with a line drawn through the points 5 comma 4 and 7 comma 5
scatter plot with points plotted at 1 comma 3, 2 comma 5, 3 comma 4, 3 comma 7, 4 comma 6, 5 comma 4, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 8, 9 comma 6, and 10 comma 8, with a line drawn through the points 1 comma 3 and 3 comma 4
scatter plot with points plotted at 1 comma 3, 2 comma 5, 3 comma 4, 3 comma 7, 4 comma 6, 5 comma 4, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 8, 9 comma 6, and 10 comma 8, with a line drawn through the points 2 comma 5 and 4 comma 6
scatter plot with points plotted at 1 comma 3, 2 comma 5, 3 comma 4, 3 comma 7, 4 comma 6, 5 comma 4, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 8, 9 comma 6, and 10 comma 8, with a line drawn through the points 1 comma 4 and 4 comma 5

1 answer

To determine which line best fits the scatter plot described, we need to look for a line that closely follows the trend of the points on the plot.

  1. Points:
    • 1, 3
    • 2, 5
    • 3, 4
    • 3, 7
    • 4, 6
    • 5, 4
    • 5, 5
    • 6, 7
    • 7, 5
    • 8, 8
    • 9, 6
    • 10, 8

Examining the provided options for the points mentioned:

  1. First Option: Between (5, 4) and (7, 5) may not capture the overall trend effectively because the points are not closely aligned with the majority of the points in the scatter plot.

  2. Second Option: Between (1, 3) and (3, 4) also does not cover the spread of the points very well.

  3. Third Option: Between (2, 5) and (4, 6) could do a little better since the points are positioned within the region but might not be capturing the main distribution effectively.

  4. Fourth Option: Between (1, 4) and (4, 5) does not seem to reflect any significant slope or meaningful direction that matches the bulk of the scatter plot.

Upon evaluating the points, plotting a line that goes through key data points (particularly around (2, 5) and (4, 6)) seems to represent a more appropriate trend of the dataset as it reflects the upward trend of the surrounding values.

Overall, the Third Option looks like the most fitting line through the data points, capturing a slope that aligns with the increasing nature of the scatter plot. Thus, the option with the line drawn through the points (2, 5) and (4, 6) shows the best fit for the data.