Determine whether the pair of lines is parallel, perpendicular, or neither. \( y=-\frac{7}{15} x+2 \) \( y=-\frac{15}{7} x-2 \)

To determine whether the given lines are parallel, perpendicular, or neither, we need to analyze their slopes. The equations of the lines are given in slope-intercept form \( y = mx + b \), where \( m \) is the slope. 1. **Identify the slopes:** - For the first line \( y = -\frac{7}{15} x + 2 \), the slope \( m_1 = -\frac{7}{15} \). - For the second line \( y = -\frac{15}{7} x - 2 \), the slope \( m_2 = -\frac{15}{7} \). 2. **Check for parallelism:** - Two lines are parallel if their slopes are equal: \( m_1 = m_2 \). - Here, \( -\frac{7}{15} \neq -\frac{15}{7} \), so the lines are not parallel. 3. **Check for perpendicularity:** - Two lines are perpendicular if the product of their slopes is \(-1\): \( m_1 \cdot m_2 = -1 \). - Calculate the product: \[ m_1 \cdot m_2 = \left(-\frac{7}{15}\right) \cdot \left(-\frac{15}{7}\right) \] Now, let's calculate this product. \[ m_1 \cdot m_2 = \frac{7 \cdot 15}{15 \cdot 7} = 1 \] Since the product of the slopes is \( 1 \), the lines are not perpendicular. 4. **Conclusion:** The lines are neither parallel nor perpendicular.