11X1 T05 04 point slope formula (2010)

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11X1 T05 04 point slope formula (2010)

  1. 1. Point Slope Formula
  2. 2. Point Slope Formula y  y1  m  x  x1 
  3. 3. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6)
  4. 4. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m 3  2 10  5  2
  5. 5. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 10  5  2
  6. 6. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2
  7. 7. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0
  8. 8. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 5 y  x 4 4
  9. 9. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 5 y  x 4 4 3 required m   4
  10. 10. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 y  3    x  2 3 5 4 y  x 4 4 3 required m   4
  11. 11. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 y  3    x  2 3 5 4 y  x 4 y  12  3 x  6 4 4 3 3x  4 y  6  0 required m   4
  12. 12. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 OR y  3    x  2 3 5 4 y  x 4 y  12  3 x  6 4 4 3 3x  4 y  6  0 required m   4
  13. 13. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 OR 3x  4 y  k  0 y  3    x  2 3 5 4 y  x 4 y  12  3 x  6 4 4 3 3x  4 y  6  0 required m   4
  14. 14. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 OR 3x  4 y  k  0 y  3    x  2 3 y  x 5 4  2, 3 : 3  2   4  3  k  0 4 4 4 y  12  3 x  6 3 3x  4 y  6  0 required m   4
  15. 15. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 OR 3x  4 y  k  0 y  3    x  2 3 y  x 5 4  2, 3 : 3  2   4  3  k  0 4 y  12  3 x  6 4 4 6  k  0 3x  4 y  6  0 required m   3 k 6 4
  16. 16. Point Slope Formula y  y1  m  x  x1  e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 46 m y  4  2  x  3 3  2 y  4  2 x  6 10  2x  y  2  0 5  2 (ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0 3 OR 3x  4 y  k  0 y  3    x  2 3 y  x 5 4  2, 3 : 3  2   4  3  k  0 4 y  12  3 x  6 4 4 6  k  0 3x  4 y  6  0 required m   3 k 6 4  3x  4 y  6  0
  17. 17. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0
  18. 18. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 9 6 y  x 4 4
  19. 19. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 9 6 y  x 4 4 4 required m   9
  20. 20. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 4 9 6 y  4    x  6 y  x 9 4 4 4 required m   9
  21. 21. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 4 9 6 y  4    x  6 y  x 9 4 4 9 y  36  4 x  24 4 required m   4 x  9 y  60  0 9
  22. 22. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4 9 6 y  4    x  6 y  x 9 4 4 9 y  36  4 x  24 4 required m   4 x  9 y  60  0 9
  23. 23. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 6 y  4    x  6 y  x 9 4 4 9 y  36  4 x  24 4 required m   4 x  9 y  60  0 9
  24. 24. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 4 required m   4 x  9 y  60  0 9
  25. 25. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9
  26. 26. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0
  27. 27. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0 To prove three lines (l, m, n) are concurrent;
  28. 28. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0 To prove three lines (l, m, n) are concurrent; (i ) solve l and m simultaneously
  29. 29. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0 To prove three lines (l, m, n) are concurrent; (i ) solve l and m simultaneously (ii ) substitute point of intersection into n
  30. 30. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0 To prove three lines (l, m, n) are concurrent; (i ) solve l and m simultaneously (ii ) substitute point of intersection into n (iii ) if it satisfies the equation, then the lines are concurrent
  31. 31. (ii) Find the equation of the line passing through (6,4) and is perpendicular to 9x – 4y + 6 =0 OR 4x  9 y  k  0 4 9 y  x 6 y  4    x  6  6, 4  : 4  6   9  4   k  0 9 4 4 9 y  36  4 x  24 60  k  0 4 k  60 required m   4 x  9 y  60  0 9  4 x  9 y  60  0 To prove three lines (l, m, n) are concurrent; (i ) solve l and m simultaneously (ii ) substitute point of intersection into n (iii ) if it satisfies the equation, then the lines are concurrent Exercise 5D; 1e, 2c, 4abc (i), 5b, 7d, 9, 11, 13, 15, 17ab (i), 18ab (ii), 19, 22, 23c, 26*

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