Question

which graph shows the line of best fit for the data? (four graphs with scatter plots and lines are shown, x - axis from 2 to 20, y - axis from 1 to 10)

Explanation:

To determine the line of best fit, we analyze the trend of the data points:

Step 1: Identify the Correlation

The data points generally show a positive correlation (as \( x \) increases, \( y \) tends to increase slightly). A positive correlation means the line of best fit should have a positive slope (rising from left to right).

Step 2: Evaluate Each Graph

• Top - Left Graph: The line has a positive slope, and the data points are reasonably distributed around it (consistent with a weak positive correlation).
• Top - Right Graph: The line has a negative slope (falling from left to right), which contradicts the positive trend of the data.
• Bottom - Left Graph: The line has a negative slope (falling from left to right), which contradicts the positive trend of the data.
• Bottom - Right Graph: The line’s slope is too shallow, and the vertical intercept (around \( y = 4 \)) does not align with the data’s vertical spread (points reach \( y = 10 \) and \( y = 1 \)).

Answer:

The top - left graph (with the positive - sloped line starting near \( (0, 5) \) and rising to \( (20, 7) \)) shows the line of best fit.