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A scatter plot is shown on the coordinate plane.

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

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

1 answer

To find the line that best fits the data points on the scatter plot, let's analyze the points provided:

The points listed are:

  • (1, 9)
  • (3, 7)
  • (4, 5)
  • (4, 6)
  • (5, 3)
  • (6, 4)
  • (7, 4)
  • (8, 4)
  • (9, 2)
  • (10, 1)

The general trend of the points appears to be a downward slope as the x-values increase. To identify the best-fitting line, we need to check the proposed lines against the overall trend of the data points.

  1. Line through (7, 4) and (9, 2): This line appears to fit the downward trend well.

  2. Line through (4, 6) and (9, 2): While this line does start higher, it also follows a downward trajectory, but may not represent the data accurately as it potentially skips key points.

  3. Line through (4, 5) and (8, 1): This line may not be an accurate representation of the data since it includes a point (8, 1) that is not plotted and extends quite low.

  4. Line through (6, 4) and (7, 4): This line is horizontal and does not fit the downward trend.

Considering these options, the line drawn through the points (7, 4) and (9, 2) likely represents the trend of the data points the best. Therefore, the first choice represents the best fit for the data.