To determine whether the two lines are parallel or perpendicular, we can compare their slopes.
The slope of line \( q \) is \( -\frac{6}{5} \), and the slope of line \( r \) is \( -\frac{5}{6} \).
1. Checking if the lines are parallel:
- Lines are parallel if their slopes are equal.
- Since \( -\frac{6}{5} \) is not equal to \( -\frac{5}{6} \), the lines are not parallel.
2. Checking if the lines are perpendicular:
- Lines are perpendicular if the product of their slopes is \( -1 \).
- Let's calculate the product of the slopes:
\[ -\frac{6}{5} \times -\frac{5}{6} = \frac{6 \times 5}{5 \times 6} = 1 \]
Since the product is \( 1 \) (not \( -1 \)), the lines are also not perpendicular.
Conclusion: The lines \( q \) and \( r \) are neither parallel nor perpendicular.