Find the slope of a line perpendicular to the line whose equation is \( 6 x+2 y=-32 \). Fully simplify your answer.

Step 1 ：\( 6x+2y=-32 \)

Step 2 ：\( y=-3x-16 \)

Step 3 ：\( m=-3 \)

Step 4 ：\( m_{\perp}=\frac{1}{3} \)