Name____________________________ date_______________________ Unit 3 Notes: Parallel and Perpendicular Lines Parallel lines have the same slope. The lines must be in slope-­‐intercept form to determine their slope. Decide if the following pairs of lines are parallel. 1. y = 4x – 1 y = 4x + 2 2. –x + 2y = 12 5x – 10y = 3 4. y = 7 y = -­‐3 5. x = 4.5 x = 8 3. 3x + 2y = 6 3x – 2y = 6 Perpendicular lines have slopes that are opposite reciprocals of each other. The lines must be in slope-­‐intercept form to determine their slope. 2
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If a line has a slope of -­‐ , the perpendicular line will have a slope of 2 2
Example: If a line has a slope of , the perpendicular line will have a slope of -­‐ Decide if the following pairs of lines are perpendicular. 1
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1. y = 5x – 1 y = -­‐ x + 3 2. y = x y = x – 2 5
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4. 4x – 5y = 10 5x – 4y = 2 7. x = 2 y = -­‐6 5. 7x – 4y = 0 -­‐4x – 7y = -­‐2 3. y = x y = -­‐x 1
6. y = 3 y = -­‐ 3
1. Write the equation of a line that is parallel to y = 3x + 1 and y-­‐intercept of -­‐5 _______________________ 2. Write the equation of a line that is perpendicular to 2x + y = 11 and has a y-­‐intercept of -­‐8. _______________________ 2
3. Write the equation of a line that is perpendicular to y = x – 1 and has the same y-­‐intercept 5
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as the line y = x + 2. 9
_______________________ 4. Write the equation of a line that is parallel to 3x – 2y = 4 and passes through the point (6, 1). _______________________ 4
5. Write the equation of a line that is perpendicular to y = -­‐ x + 6 and passes through the point (4,-­‐3) 5
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