\begin{tabular}{l} What is the slope of a line that is perpendicular to the line whose equation is \( A x+B y+C=0, A \neq 0 \) and \( B \neq 0 \) ? \\ The slope of the line perpendicular to the line \( A x+B y+C=0 \) is \\ \hline\end{tabular}

1. Write the equation of the given line: \[ Ax + By + C = 0 \] 2. Solve for \( y \) to determine the slope: \[ By = -Ax - C \quad \Longrightarrow \quad y = -\frac{A}{B} x - \frac{C}{B} \] The slope of this line is: \[ m = -\frac{A}{B} \] 3. For two perpendicular lines with slopes \( m \) and \( m_{\perp} \), the property is: \[ m \cdot m_{\perp} = -1 \] 4. Substitute \( m = -\frac{A}{B} \) and solve for \( m_{\perp} \): \[ \left(-\frac{A}{B}\right) \cdot m_{\perp} = -1 \quad \Longrightarrow \quad m_{\perp} = \frac{-1}{-\frac{A}{B}} = \frac{B}{A} \] The slope of the line perpendicular to \( Ax + By + C = 0 \) is: \[ \frac{B}{A} \]