The document discusses the point slope formula and provides examples of its use. Specifically, it: 1) Defines the point slope formula as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point. 2) Works through an example of finding the equation of the line passing through points (-3,4) and (2,-6). 3) Works through another example of finding the equation of the line passing through (2,-3) that is parallel to the line 3x + 4y - 5 = 0.

1. Point Slope Formula

2. Point Slope Formula
y  y1  m  x  x1 

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x – 4y + 6 =0

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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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*