Int. Alg. Notes
Section 3.3
Page 1 of 2
Section 3.3: Parallel and Perpendicular Lines
Big Idea: There is a relationship between the slopes of pairs of lines that are parallel and pairs of lines that are
perpendicular.
Big Skill: You should be able to determine whether two lines are parallel or perpendicular by comparing their
slopes, and derive equations of lines that are parallel or perpendicular to a given line.
Definition: Relationship between the slopes of 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.
Example:
Graph the lines y = 2x – 4 and y = 2x + 3.
Practice:
Determine if the lines 4x + y = 8 and 6x + 2y = 12 are parallel.
Determine if the lines -3x + 2y = 6 and 6x – 4y = 8 are parallel.
Write the equation of a line that is parallel to 6x – 4y = 8 and goes through the point (5, 7)
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Int. Alg. Notes
Section 3.3
Page 2 of 2
Definition: Relationship between the slopes of perpendicular lines
Two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Alternatively, their
slopes are negative reciprocals of one another. Vertical lines are perpendicular to horizontal lines.
Example:
Graph the lines y = 2x – 4 and y = -0.5x + 3.
Practice:
Determine if the lines 4x – y = 3 and x – 4y = 2 are perpendicular.
Write the equation of a line that is perpendicular to 6x – 4y = 8 and goes through the point (5, 7)
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.