11 x1 t05 06 line through pt of intersection (2012)

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11 x1 t05 06 line through pt of intersection (2012)

  1. 1. Equation of a line through a point and intersection of another two lines
  2. 2. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
  3. 3. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 3x  5 y  9  0
  4. 4. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5  3x  5 y  9  0 3x  5 y  9
  5. 5. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9
  6. 6. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14
  7. 7. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2
  8. 8. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2  2  2   y  1  0 y3
  9. 9. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2  2  2   y  1  0 y3  the lines intersect at  2,3
  10. 10. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2  2  2   y  1  0 y3 3 2  the lines intersect at  2,3 m 2  1 1  3
  11. 11. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2  2  2   y  1  0 y3 3 2 1 y  2    x  1  the lines intersect at  2,3 m 2  1 3 1  3
  12. 12. Equation of a line through a point and intersection of another two linese.g. Find the equation of the line that passes through the intersection of 2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2). 2x  y 1  0 10 x  5 y  5 ()  3x  5 y  9  0 3x  5 y  9 7x =  14 x  2  2  2   y  1  0 y3 3 2 1 y  2    x  1  the lines intersect at  2,3 m 2  1 3 1 3y  6  x 1  3 x  3y  7  0
  13. 13. Alternatively
  14. 14. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0
  15. 15. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0
  16. 16. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0
  17. 17. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0
  18. 18. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4
  19. 19. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4 5 2x  y 1  3x  5 y  9   0 4
  20. 20. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4 5 2x  y 1  3x  5 y  9   0 48 x  4 y  4  15 x  25 y  45  0
  21. 21. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4 5 2x  y 1  3x  5 y  9   0 48 x  4 y  4  15 x  25 y  45  0 7 x  21 y  49  0
  22. 22. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4 5 2x  y 1  3x  5 y  9   0 48 x  4 y  4  15 x  25 y  45  0 7 x  21 y  49  0 x  3y  7  0
  23. 23. Alternatively a1 x  b1 y  c1  k  a2 x  b2 y  c2   0 2 x  y  1  k  3x  5 y  9   0 1, 2  : 2 1   2   1  k  3 1  5  2   9   0 5  4k  0 4k  5 5 k  4 5 2x  y 1  3x  5 y  9   0 48 x  4 y  4  15 x  25 y  45  0 Exercise 5F; 2b, 3b, 6b(i), 7ab (i, iii), 9, 10, 13* 7 x  21 y  49  0 x  3y  7  0 Exercise 5G; 2 to 14 evens, 15*

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