Question

what is the slope of line pq?
what is the slope of line mn?
how are the two lines related?

Explanation:

Step1: Find the slope of line PQ

Line PQ is horizontal. For a horizontal line, the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(P(-8,2)\) and \(Q(4,2)\). Then \(m_{PQ}=\frac{2 - 2}{4-(-8)}=\frac{0}{12}=0\).

Step2: Find the slope of line MN

Line MN is vertical. For a vertical line, the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(M(8,6)\) and \(N(8,-8)\). Then \(m_{MN}=\frac{-8 - 6}{8 - 8}\), division by zero is undefined. So the slope of a vertical line is undefined.

Step3: Determine the relationship between the two lines

A horizontal line (slope \(m = 0\)) and a vertical line (slope undefined) are perpendicular to each other.

Answer:

Slope of line PQ: \(0\)
Slope of line MN: Undefined
Relationship: Perpendicular