Question

1. p(-9, -4), q(-7, -1), r(-2, 5), s(-6, -1)

| ( mleft(overleftrightarrow{pq}
ight) ) | ( mleft(overleftrightarrow{rs}
ight) ) | types of lines |

Explanation:

Step1: Calculate slope of \( \overline{PQ} \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For \( P(-9, -4) \) and \( Q(-7, -1) \), \( x_1=-9, y_1=-4, x_2=-7, y_2=-1 \).
\( m(\overline{PQ}) = \frac{-1 - (-4)}{-7 - (-9)} = \frac{3}{2} \)

Step2: Calculate slope of \( \overline{RS} \)

For \( R(-2, 5) \) and \( S(-6, -1) \), \( x_1=-2, y_1=5, x_2=-6, y_2=-1 \).
\( m(\overline{RS}) = \frac{-1 - 5}{-6 - (-2)} = \frac{-6}{-4} = \frac{3}{2} \)

Step3: Determine line type

Since \( m(\overline{PQ}) = m(\overline{RS}) \), the lines are parallel.

Answer:

\( m(\overline{PQ}) \)	\( m(\overline{RS}) \)	Types of Lines