Question

which graph shows the line of best fit for the data? (four scatter plots with lines are shown, as described in the image)

Explanation:

To determine the line of best fit, we analyze the scatter plots:

Step 1: Understand the Line of Best Fit

The line of best fit should minimize the distance between itself and all data points (red dots) and reflect the overall trend (positive/ negative) of the data.

Step 2: Analyze Each Graph

• Top - Left Graph: The line starts at \( y = 4 \) and has a shallow slope. The data points are clustered around a trend, but check other options.
• Top - Right Graph: The line starts at \( y = 5 \) and has a shallow slope. The data points are more evenly distributed around this line, matching the positive trend of the scatter plot.
• Bottom - Left Graph: The line is steeper than the top - right and does not align as well with the cluster of points (especially the lower - left points).
• Bottom - Right Graph: The line is very steep and does not reflect the gradual positive trend of the data (most points are not close to this steep line).

The top - right graph’s line best balances the distribution of data points around it, capturing the overall positive trend.

Answer:

The graph in the top - right (with the line starting near \( y = 5 \) and rising gently) shows the line of best fit.