Which of the following scatter plots suggests a linear relationship between two variables?

• A. A plot where the points form a clear curved pattern, such as a parabola ($y^2$ or $x^2$ shape).
• B. A plot where the points form a circular pattern (e.g., $x^2$ + $y^2$ = $r^2$).
• C. A plot where the points are widely scattered with no apparent pattern.
• D. A plot where the points closely follow a straight line, either upward or downward (linear: $y=ax+b$).

Answer: (D)

Verified step by step guidance

1. Understand that a linear relationship between two variables means that as one variable changes, the other variable changes at a constant rate, which is visually represented by points lying close to a straight line in a scatter plot.
2. Examine the scatter plot where points form a clear curved pattern, such as a parabola; this indicates a nonlinear relationship, not linear.
3. Look at the scatter plot where points form a circular pattern; this suggests no linear relationship because the points do not align along a straight line.
4. Consider the scatter plot where points are widely scattered with no apparent pattern; this indicates no relationship or a very weak relationship between the variables.
5. Identify the scatter plot where points closely follow a straight line, either upward (positive slope) or downward (negative slope), as this is the hallmark of a linear relationship between the two variables.