Vertical and horizontal lines
A horizontal line, parallel to the x-axis, has a slope of zero. A horizontal line is the graph of the constant polynomial function:
A vertical line, parallel to the y-axis, has an undefined slope. A vertical line is the graph of the equation:y = a
Note that this is not a function.x = k
Since the y-axis of the Cartesian plane is perpendicular the x-axis, a vertical line and a horizontal line are perpendicular. Also, any two vertical lines are parallel since they are both parallel to the vertical y-axis.
Parallel lines
If two non-vertical lines have the same slope, they are parallel. Conversely, any two non-vertical parallel lines have the same slope.
Perpendicular lines
Given two non-vertical lines with slopes m1 and m2; the lines are perpendicular if the following equation is true:
For example, a line through point {3, 4} with a positive slope of 2 ism1m2 = -1 or, m1 = -1/m2
The equation of a perpendicular line through the same point is:y = 2(x - 3) + 4
y = -0.5(x - 3) + 4