Question

1. p(-4,17), q(1,-3), r(-9,3), s(-5,4) slope of (overline{pq}) slope of (overline{rs}) 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 $P(-4,17)$ and $Q(1,-3)$:
$m_{PQ}=\frac{-3-17}{1-(-4)}=\frac{-20}{5}=-4$

Step2: Calculate slope of $\overline{RS}$

Using the slope formula for $R(-9,3)$ and $S(-5,4)$:
$m_{RS}=\frac{4-3}{-5-(-9)}=\frac{1}{4}$

Step3: Classify line relationship

Check if slopes are negative reciprocals: $-4 \times \frac{1}{4}=-1$. Lines are perpendicular.

Answer:

Slope of $\overline{PQ}$	Slope of $\overline{RS}$	Types of Lines