Table of Contents
If 2 lines are parallel, their slopes are same.
Slope is the value m in the equation of a line.
y = mx + b
The previous methods work nicely except for a vertical line.
The gradient is undefined (as we cannot divide by 0):
m = (yA − yB) / (xA − xB)
m = (7 − 0) / (7 − 7)
m = 7/0 = undefined
So just rely on the fact that:
- a vertical line is parallel to another vertical line.
- a vertical line is perpendicular to a horizontal line (and vice versa).
Not The Same Line
They may be the same line (with different equation), and so are not parallel.
To find if they are really the same line, Check their y-intercepts (where they cross the y-axis) as well as their slope:
2 lines are Perpendicular when they meet at a right angle (90°).
To find a perpendicular slope:
When a line has a slope of m, a perpendicular line has a slope of −1/m
In other words the negative reciprocal
Quick Check of Perpendicular
When we multiply a slope m by its perpendicular slope −1/m we get −1.
So to quickly check if 2 lines are perpendicular:
When we multiply their slopes, we get −1
- parallel lines: same slope
- perpendicular lines: negative reciprocal slope (−1/m)