Question

use slope to determine if lines pq and rs are parallel, perpendicular, or intersecting.
line pq
p(-9,-4) and q(-7,-1)
type your answer...
line rs
r(-2,5) and s(-6,-1)
type your answer...
types of lines
type your answer...

Explanation:

Step1: Calculate the slope of line PQ

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(P(-9,-4)\) and \(Q(-7,-1)\), we have \(x_1=-9,y_1 = - 4,x_2=-7,y_2=-1\).

$$m_{PQ}=\frac{-1-(-4)}{-7-(-9)}=\frac{-1 + 4}{-7 + 9}=\frac{3}{2}$$

Step2: Calculate the slope of line RS

For points \(R(-2,5)\) and \(S(-6,-1)\), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1=-2,y_1 = 5,x_2=-6,y_2=-1\).

$$m_{RS}=\frac{-1-5}{-6-(-2)}=\frac{-6}{-4}=\frac{3}{2}$$

Step3: Determine the relationship between the lines

Since \(m_{PQ}=m_{RS}=\frac{3}{2}\), when two lines have the same slope, they are parallel.

Answer:

The slope of line \(PQ\) is \(\frac{3}{2}\), the slope of line \(RS\) is \(\frac{3}{2}\), and the lines \(PQ\) and \(RS\) are parallel.