The equation \( y = \frac{1}{2}x \) is indeed a linear relationship. In this equation:
- \( y \) is directly proportional to \( x \).
- The coefficient \( \frac{1}{2} \) indicates the slope of the line, and there is no constant term added (i.e., the y-intercept is 0).
Linear equations can generally be described in the form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. Since \( \frac{1}{2} \) is the slope and there is no additional constant (i.e., \( b = 0 \)), this equation describes a straight line passing through the origin (0,0).
Thus, \( y = \frac{1}{2}x \) represents a linear relationship.