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A scatter plot is shown on the coordinate plane.

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

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

1 answer

To determine which line best fits the data represented by the scatter plot points you provided, let's analyze the points:

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

We can estimate where a line of best fit might be based on the general trend of these points. The points represent a trend that is decreasing as we move from left to right, though there are some fluctuations.

Next, let's evaluate each option based on the provided coordinates to see which one matches the trend:

  1. Line through (7, 6) and (10, 5): This line would have a negative slope and seems to follow the downward trend in the data.

  2. Line through (2, 6) and (5, 5): This line has a slight negative slope and does capture a bit of the decreasing trend, but it might not fully represent the overall relationship of the other points.

  3. Line through (2, 7) and (7, 5): This line has a moderate negative slope and could represent some of the data trend, though it may not match very well as we see values jumping up and down in that region.

  4. Line through (1, 8) and (10, 3): This line has a strong negative slope and encompasses the start (1, 8) to a lower value (10, 3). While it fits the overall decreasing trend, it might be too steep and not accurately represent the clustering of points, particularly those around the x-coordinates 4 to 8.

Based on this assessment, the first option, a line passing through (7, 6) and (10, 5), would best fit the trend of the scatter plot, as it closely follows the slope and represents a more localized section of the dataset without being too steep.

Therefore, the correct selection for the line that fits the data is: the first option.