Equations of Lines

Definition of Slope

The slope of the nonvertical line passing through the two points and is the number defined by .

We often write

Special cases:

A horizontal line has a slope of zero.

The slope of a vertical line is not defined.

Formats for the equation of a line

· Point-Slope Formula: A line having a slope of m and passing through the point has the equation

· Slope-Intercept Formula: A line having a slope of m and y-intercept b.

· Standard Form: . Note: If A = 0 then this equation could be written as , which is the equation of the horizontal line with y-intercept . If B = 0, then the equation can be written , which represents the vertical line with x-intercept .

Math 41, Section 1.6 page 2

· In general the equation of a horizontal line through the point is

· In general the equation of a vertical line through the point is

Relationships between parallel and perpendicular lines

Let and denote the slopes of two distinct nonvertical lines. Then:

1. The lines are parallel if and only if .

2. The lines are perpendicular if and only if .