To determine the best line of fit for the given scatter plot of points:
- (1, 7)
- (1, 8)
- (2, 9)
- (3, 6)
- (4, 8)
- (5, 5)
- (5, 6)
- (6, 7)
- (7, 5)
- (8, 7)
- (9, 4)
- (10, 2)
We need to analyze how these points are spread out across the x-y plane and what the overall trend of the data seems to be.
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The points appear to have some variation, but overall, we might find a trend where y decreases as x increases after a certain point, especially towards the end where points like (9, 4) and (10, 2) significantly drop.
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We can find key pairs of points that might be good candidates for drawing a line of fit.
Let's analyze the proposed lines:
- First option: Line through (3, 6) and (5, 6) - This line is horizontal and doesn't capture the decreasing trend in the later points.
- Second option: Line through (2, 9) and (6, 7) - They seem to keep a decent connection with some of the higher y-values, but it may not capture the overall trend through the lower points well.
- Third option: Line through (1, 7) and (3, 6) - This line starts with a higher point but heads downward slightly. It may not account for some of the peaks at (2, 9) and (4, 8).
- Fourth option: Line through (1, 8) and (7, 5) - This option captures an upward trend that begins but ultimately heads downwards, reflecting some of the declining values, especially accounting for points toward (10, 2).
The best fit line should start higher and then trend down to capture the overall tendency of the points, especially toward the right side of the scatter plot.
Thus, the fourth option (line through about 1,8 and 7,5) appears to be the most suitable line to fit the data, as it reflects both the initial rise and the subsequent decrease as x increases.