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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.