A scatter plot is shown on the coordinate plane.

Question

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

Which of the following graphs shows a line on the scatter plot that fits the data?

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 7 and 3 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 8 and 5 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 2 comma 5 and 4 comma 4
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 4.5 and 2 comma 4.5

Answer 1

To determine which line best fits the scatter plot with the given points, we need to evaluate the general trend of the scatter points provided:

• The points appear to have a general trend of decreasing as the x-values increase, especially in the latter half of the dataset.
• Points like (1, 7) and (1, 8) are higher in the y-values, while points like (8, 2) and (10, 2) are lower.

Let's analyze the options provided:

1. Line through (1, 7) and (3, 6): This line would suggest a slight downward trend but doesn't seem to follow the overall trend of the points well as it doesn’t capture the decline in the latter half.

2. Line through (1, 8) and (5, 6): This line suggests a slight increase or a more horizontal line, not matching well with the trend of decreasing points.

3. Line through (2, 5) and (4, 4): This line suggests a downward slope and aligns better with the overall trend of the points, which shows a decreasing trend in that region.

4. Line through (1, 4.5) and (2, 4.5): This line is horizontal and does not fit well with the points at all.

Given these analyses, the graph that likely shows a line on the scatter plot that best fits the data is:

The scatter plot with a line drawn through about (2, 5) and (4, 4).

This line captures the downward trend in the scatter of points more effectively than the others.