Which of these lines is Wizard perpendicular to the line \( y \) \( =3 x+2 \) ?

1. The given line is \[ y = 3x + 2, \] which has a slope \( m = 3 \). 2. Two lines are perpendicular if the product of their slopes is \(-1\). That is, if a line with slope \( m_1 \) is perpendicular to a line with slope \( m_2 \), then \[ m_1 \cdot m_2 = -1. \] 3. Let \( m_{\perp} \) be the slope of the line perpendicular to the given line. Then, \[ 3 \cdot m_{\perp} = -1. \] 4. Solving for \( m_{\perp} \): \[ m_{\perp} = -\frac{1}{3}. \] 5. Therefore, among the options provided, the line with slope \(-\frac{1}{3}\) is perpendicular to the line \[ y = 3x + 2. \] Any line with the form \[ y = -\frac{1}{3}x + b, \] where \( b \) is any constant, will be perpendicular to the line \( y = 3x+2 \).