To determine whether the relationship represented by the equation \( y = |2x| \) is linear or not, we need to analyze its form.
A linear relationship can typically be expressed in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In such relationships, the graph of the equation will produce a straight line.
The equation \( y = |2x| \) represents the absolute value of \( 2x \). The absolute value function creates a V-shape graph that opens upwards, which indicates that the relationship is not linear.
Specifically, the graph of this equation consists of two linear segments:
- For \( x \geq 0 \), \( y = 2x \)
- For \( x < 0 \), \( y = -2x \)
These segments intersect at the origin (0, 0), but because the graph has a "corner" point at that intersection and does not form a continuous straight line, it indicates that the relationship is not linear.
In conclusion, the equation \( y = |2x| \) does not represent a linear relationship.