Math 1.7 Parallel and Perpendicular Lines
How to determine if two lines are parallel
Find the slope and y-intercept of each line by writing their equations in slope intercept form. *If the slopes are the same but the y-intercept are different, then the lines are parallel. If the lines have different slopes, they are not parallel.*
Word Smart on Parallel Lines
The words *if and only if* given in the definition mean that there are two statements being made: (1) If two nonvertical lines are parallel, then their slopes are equal and they have different y-intercepts. (2) If two nonvertical lines have equal slopes and different y-intercepts, then they are parallel.
Define Perpendicular Lines
Two lines that intersect at a right angle (90°), are *perpendicular*. We use the slopes of the lines to determine whether two lines are perpendicular.
Parallel Lines
Two nonvertical lines are *parallel* if and only if their slopes are equal and they have different y-intercepts. Vertical lines are parallel if they have different x-intercepts.
Perpendicular Lines
Two nonvertical lines are *perpendicular* if and only if the product of their slopes is -1. Alternatively, two nonvertical lines are perpendicular if their slopes are negative reciprocals of each other. Any vertical line is perpendicular to any horizontal line.
Define Parallel Lines
When two lines (in the Cartesian plane) do not intersect (that is, they have no points in common), they are said to be *parallel.*