A scatter plot is shown on the coordinate plane.

Question

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

Answer 1

To determine which line best fits the given scatter plot points, we should look for a line that represents the general trend of the plotted points.

The points are:

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

We want a line that approximately averages the y-values for each x-value.

Let's analyze each option:

1. Line through (5, 4) and (7, 5): This line has a slight upward slope but does not capture much of the overall trend of the data, especially at lower x-values.

2. Line through (1, 3) and (3, 4): This line has a very low slope and does not adequately cover the higher y-values of the other points.

3. Line through (2, 5) and (4, 6): This line has a moderate positive slope and captures part of the upward trend, but it may not fit well with many points.

4. Line through (1, 4) and (4, 5): This line also has a lower slope, failing to capture the increasing y-values present in the plot.

The best option for a line that fits the trend of the given data would likely be the third option (line through (2, 5) and (4, 6)), as it has a reasonable slope and aligns more closely with the cluster of points around that area compared to the other options.

Ultimately, although none of the lines may fit perfectly, the line through (2, 5) and (4, 6) seems to best represent an overall trend.