Question

1. ( p(-9,-4), q(-7,-1), r(-2,5), s(-6,-1) ) ( overline{p q} ) and ( overline{r s} ) are ( square ), because the slope of ( overline{p q} ) is ( m=square ) and the slope of ( overline{r s} ) is ( m=square ). for the first text box, only type either parallel, perpendicular, or neither. make sure that you spell the word correctly so it will count your answer as correct.

Explanation:

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

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

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

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

Step3: Determine the relationship between \(\overline{PQ}\) and \(\overline{RS}\)

Since \(m_{PQ}=m_{RS}=\frac{3}{2}\), two lines with equal slopes are parallel.

Answer:

parallel, \(\frac{3}{2}\), \(\frac{3}{2}\)