Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations.

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Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations of parallel and perpendicular lines

Property: Slopes of Parallel Lines Non-vertical lines are parallel if they have the same slope and different y-intercepts. Any two vertical lines are parallel

Are the following lines parallel? 1)y = 5x + 5; y = 5x – 10 2) y = -x; y – 3 = -1(x + 9) 3)4x + 2y = 6; -6x + 3y = 1

Find the slope of the line parallel to the graph of each equation. 1) y = 4x + 22) y = -9x – 13 3) y – 3 = 04) -5x + 5y = 4

Writing equations of || lines Write an equation of a line || to y = 3x + 2 and passes through the point (-1, 4)

Writing equations of || lines Write an equation of a line || to y = ½ x + 2 and passes through the point (6, -3)

Property: Slopes of Perpendicular Lines Two lines are perpendicular if the product of their slopes is -1. That is, if their slopes are opposite reciprocals. A vertical and a horizontal line are also perpendicular

Are the following lines perpendicular? 1)y = 6x; y = -1/6x + 2 2)y = 3x – 2; 3y = -x – 11 3)y = -5x + 7; y = -1/5x + 2

Find the slope of the line perpendicular to the graph of each equation 1)y = 2/3x – 42) y – 4 = -7(x + 2) 3) x – 6y = 154) 3y = -x -11

Writing equations of | lines Write an equation of a line that is | to y – 2 = 2(x + 3) and passes through the point (6, -1)

Writing equations of | lines Write an equation of a line that is | to and passes through the point (6, -1)

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