Question

directions: use the slope to determine if lines pq and rs are parallel, perpendicular, or neither.

p(-3,-4); q(-7,-1); r(-2,5); s(-6,-1)

m(pq) m(rs) type of lines

Explanation:

Step1: Calculate the slope of line \(PQ\)

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

Step2: Calculate the slope of line \(RS\)

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

Answer:

\(m(PQ)=-\frac{3}{4}\), \(m(RS)=\frac{3}{2}\)