Question

2.
line ( l ) has a slope of ( -\frac{2}{1} ), the segments must have an
opposite - reciprocal slope of ( +\frac{1}{2} ).
3.
line ( l ) has a slope of , the segments must have an
opposite - reciprocal of .

Explanation:

Step1: Find the slope of line \( l \)

Use the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's assume two points on line \( l \). Suppose the line \( l \) passes through points \((x_1,y_1)\) and \((x_2,y_2)\). If we count the rise and run on the grid, for line \( l \), the rise \( \Delta y = 3 \) and the run \( \Delta x=1 \). So the slope \( m=\frac{3}{1}=3 \).

Step2: Find the opposite - reciprocal slope

The formula for the opposite - reciprocal of a number \( m \) is \( -\frac{1}{m} \). Given \( m = 3 \), the opposite - reciprocal is \( -\frac{1}{3} \).

Answer:

Line \( l \) has a slope of \( 3 \), the segments must have an opposite - reciprocal of \( -\frac{1}{3} \).