\[ \begin{array}{l}\text { Determine whether the pair of lines is parallel, perpendicular, or neither. } \\ y=\frac{9}{17} x-8 \\ y=-\frac{9}{17} x-8\end{array} \]

To determine whether the given pair of lines is parallel, perpendicular, or neither, we need to analyze their slopes. The equations of the lines are: 1. \( y = \frac{9}{17} x - 8 \) 2. \( y = -\frac{9}{17} x - 8 \) ### Step 1: Identify the slopes From the equations, we can see that the slope \( m_1 \) of the first line is \( \frac{9}{17} \) and the slope \( m_2 \) of the second line is \( -\frac{9}{17} \). ### Step 2: Determine the relationship between the slopes - **Parallel Lines**: Two lines are parallel if their slopes are equal, i.e., \( m_1 = m_2 \). - **Perpendicular Lines**: Two lines are perpendicular if the product of their slopes is \( -1 \), i.e., \( m_1 \cdot m_2 = -1 \). ### Step 3: Calculate the product of the slopes Let's calculate the product of the slopes: \[ m_1 \cdot m_2 = \left(\frac{9}{17}\right) \cdot \left(-\frac{9}{17}\right) \] Now, we will perform the multiplication: \[ m_1 \cdot m_2 = -\frac{81}{289} \] ### Step 4: Analyze the results Since \( -\frac{81}{289} \) is not equal to \( -1 \), the lines are not perpendicular. Additionally, since the slopes \( \frac{9}{17} \) and \( -\frac{9}{17} \) are not equal, the lines are not parallel. ### Conclusion The pair of lines is neither parallel nor perpendicular.