Parallel And Perpendicular Lines

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Parallel And Perpendicular Lines

  1. 1. Parallel and Perpendicular Lines
  2. 2. Teacher Page <ul><li>Content: Write the equation of a parallel or perpendicular line to a given line, in slope intercept form. </li></ul><ul><li>Grade Level: Algebra 2/Geometry </li></ul><ul><li>Creator: Don Sutcliffe </li></ul><ul><li>Other – Print slides 13-20 as a handout for students to take notes. </li></ul>
  3. 3. Parallel Lines <ul><li>Two non-vertical lines are parallel if and only if their slopes are equal. </li></ul><ul><ul><li>If l 1 ║ l 2 , then m 1 = m 2 . </li></ul></ul><ul><ul><li>If m 1 = m 2 , then l 1 ║ l 2 . </li></ul></ul>l 1 l 2 m 1 m 2
  4. 4. Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2. <ul><li>m = 2/3 and the point is (3,6) </li></ul><ul><li>y = mx+b </li></ul><ul><li>6 = 2/3(3)+b </li></ul><ul><li>6 = 2+b </li></ul><ul><li>4 = b </li></ul><ul><li>y = 2/3x+4 </li></ul>
  5. 5. Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4. <ul><li>m = -2 and the point is (4,-5) </li></ul><ul><li>y = mx+b </li></ul><ul><li>-5 = -2(4)+b </li></ul><ul><li>-5 = -8+b </li></ul><ul><li>3 = b </li></ul><ul><li>y = -2x+3 </li></ul>
  6. 6. Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1. <ul><li>m=1/3 and the point is (-6,4) </li></ul><ul><li>y =1/3x+6 </li></ul>
  7. 7. Perpendicular Lines <ul><li>Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. </li></ul><ul><ul><li>If l 1 ┴ l 2 , then m 1 ● m 2 = -1. </li></ul></ul><ul><ul><li>If m 1 ● m 2 = -1, then l 1 ┴ l 2 . </li></ul></ul>l 1 l 2 m 2 m 1 Slopes are negative reciprocals
  8. 8. Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3. <ul><li>m = -1/2 and the point is (6,-5) </li></ul><ul><li>y = mx+b </li></ul><ul><li>-5 = -1/2(6)+b </li></ul><ul><li>-5 = -3+b </li></ul><ul><li>-2 = b </li></ul><ul><li>y = -1/2x-2 </li></ul>
  9. 9. Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1. <ul><li>m = -3/2 and the point is (6,-7) </li></ul><ul><li>y = mx+b </li></ul><ul><li>-7 = -3/2(6)+b </li></ul><ul><li>-7 = -9+b </li></ul><ul><li>2 = b </li></ul><ul><li>y = -3/2x+2 </li></ul>
  10. 10. Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6. <ul><li>m = -1 and the point is (-4,-3) </li></ul><ul><li>y = -x-7 </li></ul>
  11. 11. End Show
  12. 12. Parallel Lines <ul><li>Two non-vertical lines are parallel if and only if their slopes are equal. </li></ul><ul><ul><li>If l 1 ║ l 2 , then m 1 = m 2 . </li></ul></ul><ul><ul><li>If m 1 = m 2 , then l 1 ║ l 2 . </li></ul></ul>l 1 l 2 m 1 m 2
  13. 13. Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2. <ul><li>m = _____ and the point is (__,__) </li></ul><ul><li>y = mx+b </li></ul>
  14. 14. Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4. <ul><li>m = ____ and the point is (__,__) </li></ul>
  15. 15. Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1. <ul><li>m=___ and the point is (__,__) </li></ul>
  16. 16. Perpendicular Lines <ul><li>Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. </li></ul><ul><ul><li>If l 1 ┴ l 2 , then m 1 ● m 2 = -1. </li></ul></ul><ul><ul><li>If m 1 ● m 2 = -1, then l 1 ┴ l 2 . </li></ul></ul>l 1 l 2 m 2 m 1
  17. 17. Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3. <ul><li>m = ___ and the point is (__,-__) </li></ul>
  18. 18. Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1. <ul><li>m = ____ and the point is (__, __) </li></ul>
  19. 19. Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6. <ul><li>m = ___ and the point is (__,__) </li></ul>

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