Question

1. p(-3,14), q(2,-1), r(4,8), s(-2,-10)

slope of (overline{pq})
slope of (overline{rs})
types of lines

Explanation:

Step1: Calculate slope of $\overline{PQ}$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ for $P(-3,14), Q(2,-1)$:
$$m_{PQ}=\frac{-1-14}{2-(-3)}=\frac{-15}{5}=-3$$

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

Use slope formula for $R(4,8), S(-2,-10)$:
$$m_{RS}=\frac{-10-8}{-2-4}=\frac{-18}{-6}=3$$

Step3: Classify line relationship

Compare $m_{PQ}=-3$ and $m_{RS}=3$: they are not equal (not parallel) and their product is $-3\times3=-9
eq-1$ (not perpendicular).

Answer:

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