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Chapter 6.5

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Chapter 6.5

  1. 1. 5.5 Parallel and Perpendicular Lines SWBAT verbally tell me how the slope of parallel lines and perpendicular lines are related. They can find the equation of a line parallel/perpendicular to a given line that passes through a given point. http://apod.nasa.gov/apod/ The Dark Doodad Nebula
  2. 2. Mini Quiz 45 1.Find the reciprocal of each fraction a. 1 2 b. 4 3 c. 1 − 3 d. 5 − 2 2.Find the slope and y-intercept of each equation 5 a. y = x + 4 4 5 b. y = x − 8 3 c. y = 6 x d. y = 6 x + 2
  3. 3. Quick Review/Preview 1. What is the Slope-Intercept Form? y = mx + b 2. What is the Standard Form? Ax + By = C 3. What is the Point-Slope Form? y – y1 = m(x – x1) 4. Find the “negative reciprocal” of each fraction 2 3 7 1 2 4 3 5 a. b. − c. − − = 2 d. − 5 7 3 2 1 3 4 2
  4. 4. Overview Parallel Lines and Perpendicular Lines  Property of their slopes  Write equations for each type of lines 
  5. 5. Parallel Lines Parallel Lines - lines that never intersect What is the slope of the red line? 1/2 What is the slope of the blue line? 1/2 Parallel Lines have the same slope!
  6. 6. Parallel Lines Determine if the lines are parallel 1 1. 2 x + 6 y = 12 and y = − x + 5 3 2x + 6y = 12 6y = -2x + 12 1 y = − x+2 3 yes
  7. 7. Parallel Lines Determine if the lines are parallel 3 2. 6 x + 8 y = −24 and y = x − 3 4 6x + 8y = -24 8y = -6x – 24 3 y = − x +3 4 No
  8. 8. Parallel Lines Determine if the lines are parallel 2 3. 4 x + 6 y = −2 and y = x −8 3 4x + 6y = -2 6y = -4x – 2 2 1 y = − x− 3 3 No
  9. 9. Equations of Parallel Lines 4. Write an equation for the line that 3 contains (5, 1) and is parallel to y = x − 4 5 3 m= 5 3 y − 1 = ( x − 5) 5
  10. 10. Equations of Parallel Lines 5. Write an equation for the line that contains (2, -6) and is parallel to y = 3x + 9 m=3 y + 6 = 3(x – 2)
  11. 11. Equations of Parallel Lines 6. Write an equation for the line that 1 contains (-4, 3) and is parallel to y = x + 7 2 1 m= 2 1 y − 3 = ( x + 4) 2
  12. 12. Perpendicular Lines Perpendicular Lines – lines that intersect to form right angles What is the slope of the red line? -1/4 What is the slope of the blue line? 4/1 Perpendicular Lines have negative reciprocal slope!
  13. 13. Perpendicular Lines What is the slope of the perpendicular line? 2 7. y = x − 8 5 1 8. y = − x 5 9. y = −2 x − 7 -5/2 5/1 = 5 1/2
  14. 14. Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 1 m=− 5 1 y+2=− x 5
  15. 15. Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to 3 y = x+1 4 4 m =− 3 4 y − 8 = − ( x − 1) 3
  16. 16. Equations of Perpendicular Lines 12. Find the equation of the line that contains (2, -3) and is perpendicular to 1 y = − x+ 6 2 m=2 y + 3 = 2(x – 2)
  17. 17. Perpendicular Lines 13. Determine if the lines are perpendicular: 2 y = x + 1 and 3 y + 2 x = 4 3 3y + 2x = 4 3 y = −2 x + 4 2 4 y =− x+ 3 3 No 14. Determine if the lines are perpendicular: 4 y = x − 5 and 4 y + 3 x = 9 3 4y + 3 x = 9 4 y = −3 x + 9 y =− 3 9 x+ 4 4 Yes

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