Question

consider the line $y = x + 2$.
what is the slope of a line parallel to this line?
what is the slope of a line perpendicular to this line?
slope of a parallel line:
slope of a perpendicular line:

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = x + 2 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. Here, the slope \( m = 1 \). So the slope of a line parallel to this line is also 1.

Step2: Recall slope of perpendicular lines

The product of the slopes of two perpendicular lines is - 1. Let the slope of the perpendicular line be \( m_{perp} \). We know that \( m\times m_{perp}=- 1 \), and \( m = 1 \). So \( 1\times m_{perp}=-1\), which gives \( m_{perp}=-1 \).

Answer:

Slope of a parallel line: \( 1 \)
Slope of a perpendicular line: \( - 1 \)