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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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)
46
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*