Which of the following scatterplots best represents a negative linear relationship between $x$ and $y$?

• A. A scatterplot where the points trend upward from left to right, forming a straight line.
• B. A scatterplot where the points trend downward from left to right, forming a straight line.
• C. A scatterplot where the points form a U-shaped curve.
• D. A scatterplot where the points are randomly scattered with no apparent pattern.

Answer: (B)

Verified step by step guidance

1. Understand what a negative linear relationship means: as the value of the variable \( x \) increases, the value of the variable \( y \) decreases in a consistent, straight-line pattern.
2. Visualize the scatterplot: for a negative linear relationship, the points should form a pattern that slopes downward from left to right, indicating that higher \( x \) values correspond to lower \( y \) values.
3. Compare the options: a scatterplot trending upward from left to right shows a positive linear relationship, not negative.
4. Recognize that a U-shaped curve indicates a nonlinear relationship, which is not linear and therefore not negative linear.
5. Identify that randomly scattered points with no pattern indicate no relationship between \( x \) and \( y \), so this does not represent a negative linear relationship.