Question

1. use the slope to determine if lines pq and rs are parallel, perpendicular, or neither. show your work for full credit. p(-9, -4), q(-7, -1), r(-2, 5), s(-6, -1)

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of line PQ

For points $P(-9,-4)$ and $Q(-7,-1)$, $m_{PQ}=\frac{-1-(-4)}{-7 - (-9)}=\frac{-1 + 4}{-7+9}=\frac{3}{2}$.

Step3: Calculate slope of line RS

For points $R(-2,5)$ and $S(-6,-1)$, $m_{RS}=\frac{-1 - 5}{-6-(-2)}=\frac{-6}{-4}=\frac{3}{2}$.

Step4: Determine the relationship

Since $m_{PQ}=m_{RS}=\frac{3}{2}$, the lines PQ and RS are parallel.

Answer:

Parallel