Consider the equation \( 7 x+9 y=-18 \) A line parallel to the above line would have a slope of A line perpendicular to the above line would have a slope of Submit Question

1. **Determine the slope of the given line:** The equation of the line is \[ 7x + 9y = -18. \] Solve for \( y \) in terms of \( x \): \[ 9y = -7x - 18, \] \[ y = -\frac{7}{9}x - 2. \] Thus, the slope of the given line is \[ m = -\frac{7}{9}. \] 2. **Slope of a line parallel to the given line:** Lines that are parallel have the same slope. Therefore, the slope of a line parallel to the given line is \[ m_{\text{parallel}} = -\frac{7}{9}. \] 3. **Slope of a line perpendicular to the given line:** Lines that are perpendicular have slopes that are negative reciprocals. Thus, the slope of a line perpendicular to the given line is \[ m_{\text{perp}} = -\frac{1}{m} = -\frac{1}{-\frac{7}{9}} = \frac{9}{7}. \] **Final Answers:** - A line parallel to the given line has slope: \( -\frac{7}{9} \). - A line perpendicular to the given line has slope: \( \frac{9}{7} \).