Question

slope to solve problems with parallel and perpendicular lines
what is the slope of line pq?
pe of line mn?
how are the two lines related?

Explanation:

Step1: Find coordinates of points P and Q

Let \(P(-8,2)\) and \(Q(4,2)\) (assuming \(y -\) coordinate is \(2\) as the line \(PQ\) is on the same horizontal level).
Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)=(-8,2)\) and \((x_2,y_2)=(4,2)\)

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

Substitute into the formula: \(m=\frac{2 - 2}{4-(-8)}=\frac{0}{12}=0\)

Step3: Find coordinates of points M and N

Assume \(M(6,6)\) and \(N(6,-8)\) (since the line \(MN\) is vertical).
Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)=(6,6)\) and \((x_2,y_2)=(6,-8)\)
\(m=\frac{-8 - 6}{6 - 6}=\frac{-14}{0}\), which is undefined (vertical line)

Step4: Determine the relationship between \(PQ\) and \(MN\)

A horizontal line (\(PQ\), slope \(m = 0\)) and a vertical line (\(MN\), slope undefined) are perpendicular.

Answer:

Slope of \(PQ\): \(0\); Slope of \(MN\): undefined; Relationship: perpendicular.