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A scatter plot is shown on the coordinate plane.

scatter plot with points at 1 comma 6, 2 comma 4, 3 comma 2, 3 comma 6, 4 comma 1, 5 comma 4, 6 comma 2, and 9 comma 2

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

1 answer

To determine which line best fits the scatter plot data based on the coordinates provided, we can analyze the points given:

  1. \( (1, 6) \)
  2. \( (2, 4) \)
  3. \( (3, 2) \)
  4. \( (3, 6) \)
  5. \( (4, 1) \)
  6. \( (5, 4) \)
  7. \( (6, 2) \)
  8. \( (9, 2) \)

A good fitting line will ideally minimize the distance to the most points. Considering the proposed lines:

  1. Line through \( (1, 6) \) and \( (5, 4) \): This line has a downward slope and passes through points that are higher on the y-axis, as it captures \( (1, 6) \) and goes down to \( (5, 4) \). This seems reasonable since those two points align well with the data trend.

  2. Line through \( (3, 4) \) and \( (7, 2) \): This line might intersect some of the points, but it doesn’t seem to best represent the overall trend based on the scattered points provided.

  3. Line through \( (1, 3) \) and \( (5, 3) \): This line is horizontal and would not capture the trend or slope of the points effectively.

  4. Line through \( (1, 6) \) and \( (3, 2) \): While this line touches two points, it may not effectively capture the overall trend across the scatter plot's data.

Based on this analysis, the first option, which shows a line passing through the coordinates \( (1, 6) \) and \( (5, 4) \), is likely the line that best fits the overall trend seen in the scatter plot data, as it represents the downward trend evident in most of the points.