Question

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

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line PQ, since it is a horizontal line (all y - values are the same), if we take two points $(x_1,y)$ and $(x_2,y)$ on line PQ, then $m_{PQ}=\frac{y - y}{x_2 - x_1}=0$.

Step2: Analyze line MN

Line MN is a vertical line. For a vertical line, if we take two points $(x,y_1)$ and $(x,y_2)$ on it, the slope formula gives $m_{MN}=\frac{y_2 - y_1}{x - x}$, and division by zero is undefined, so the slope of line MN is undefined.

Step3: Determine line - relationship

The product of the slopes of two perpendicular lines is - 1. A horizontal line (slope = 0) and a vertical line (slope is undefined) are perpendicular because the condition for perpendicularity holds in the sense that a horizontal line has a "run" but no "rise" and a vertical line has a "rise" but no "run".

Answer:

What is the slope of line PQ? 0
What is the slope of line MN? undefined
How are the two lines related? The lines are perpendicular.