Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel...
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Transcript of Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel...
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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
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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
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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
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Find the slope of the line parallel to the graph of each equation.
1) y = 4x + 2 2) y = -9x – 13
3) y – 3 = 0 4) -5x + 5y = 4
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Writing equations of || lines
• Write an equation of a line || to y = 3x + 2 and passes through the point (-1, 4)
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Writing equations of || lines
• Write an equation of a line || to y = ½ x + 2 and passes through the point (6, -3)
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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
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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
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Find the slope of the line perpendicular to the graph of each equation
1) y = 2/3x – 4 2) y – 4 = -7(x + 2)
3) x – 6y = 15 4) 3y = -x -11
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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)
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Writing equations of | lines
• Write an equation of a line that is | to and passes through the point (6, -1)