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11X1 T05 04 point slope formula (2010)
- 3. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
- 4. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½
ο3 ο 2
10
ο½
ο5
ο½ ο2
- 5. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
10
ο½
ο5
ο½ ο2
- 6. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
- 7. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0
- 8. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0
3 5
y ο½ο xο«
4 4
- 9. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0
3 5
y ο½ο xο«
4 4
3
required m ο½ ο
4
- 10. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3
y ο« 3 ο½ ο ο¨ x ο 2ο©
3 5 4
y ο½ο xο«
4 4
3
required m ο½ ο
4
- 11. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3
y ο« 3 ο½ ο ο¨ x ο 2ο©
3 5 4
y ο½ο xο« 4 y ο« 12 ο½ ο3 x ο« 6
4 4
3 3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
4
- 12. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3 OR
y ο« 3 ο½ ο ο¨ x ο 2ο©
3 5 4
y ο½ο xο« 4 y ο« 12 ο½ ο3 x ο« 6
4 4
3 3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
4
- 13. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3 OR 3x ο« 4 y ο« k ο½ 0
y ο« 3 ο½ ο ο¨ x ο 2ο©
3 5 4
y ο½ο xο« 4 y ο« 12 ο½ ο3 x ο« 6
4 4
3 3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
4
- 14. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3 OR 3x ο« 4 y ο« k ο½ 0
y ο« 3 ο½ ο ο¨ x ο 2ο©
3
y ο½ο xο«
5 4 ο¨ 2, ο3ο© : 3 ο¨ 2 ο© ο« 4 ο¨ ο3ο© ο« k ο½ 0
4 4 4 y ο« 12 ο½ ο3 x ο« 6
3 3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
4
- 15. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3 OR 3x ο« 4 y ο« k ο½ 0
y ο« 3 ο½ ο ο¨ x ο 2ο©
3
y ο½ο xο«
5 4 ο¨ 2, ο3ο© : 3 ο¨ 2 ο© ο« 4 ο¨ ο3ο© ο« k ο½ 0
4 y ο« 12 ο½ ο3 x ο« 6
4 4 ο6 ο« k ο½ 0
3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
3 k ο½6
4
- 16. Point Slope Formula
y ο y1 ο½ m ο¨ x ο x1 ο©
e.g. (i) Find the equation of the line passing through (β3,4) and (2,β6)
4ο«6
mο½ y ο 4 ο½ ο2 ο¨ x ο« 3ο©
ο3 ο 2
y ο 4 ο½ ο2 x ο 6
10
ο½ 2x ο« y ο« 2 ο½ 0
ο5
ο½ ο2
(ii) Find the equation of the line passing through (2,β3) and is parallel to
3x + 4y β 5 =0 3 OR 3x ο« 4 y ο« k ο½ 0
y ο« 3 ο½ ο ο¨ x ο 2ο©
3
y ο½ο xο«
5 4 ο¨ 2, ο3ο© : 3 ο¨ 2 ο© ο« 4 ο¨ ο3ο© ο« k ο½ 0
4 y ο« 12 ο½ ο3 x ο« 6
4 4 ο6 ο« k ο½ 0
3x ο« 4 y ο« 6 ο½ 0
required m ο½ ο
3 k ο½6
4 ο 3x ο« 4 y ο« 6 ο½ 0
- 17. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
- 18. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
9 6
y ο½ xο«
4 4
- 19. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
9 6
y ο½ xο«
4 4
4
required m ο½ ο
9
- 20. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
4
9 6 y ο 4 ο½ ο ο¨ x ο 6ο©
y ο½ xο« 9
4 4
4
required m ο½ ο
9
- 21. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
4
9 6 y ο 4 ο½ ο ο¨ x ο 6ο©
y ο½ xο« 9
4 4 9 y ο 36 ο½ ο4 x ο« 24
4
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9
- 22. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR
4
9 6 y ο 4 ο½ ο ο¨ x ο 6ο©
y ο½ xο« 9
4 4 9 y ο 36 ο½ ο4 x ο« 24
4
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9
- 23. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9 6 y ο 4 ο½ ο ο¨ x ο 6ο©
y ο½ xο« 9
4 4 9 y ο 36 ο½ ο4 x ο« 24
4
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9
- 24. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24
4
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9
- 25. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9
- 26. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 0
- 27. (ii) Find the equation of the line passing through (6,4) and is
perpendicular to 9x β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 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 β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 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 β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 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 β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 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 β 4y + 6 =0
OR 4x ο« 9 y ο« k ο½ 0
4
9
y ο½ xο«
6 y ο 4 ο½ ο ο¨ x ο 6ο© ο¨ 6, 4 ο© : 4 ο¨ 6 ο© ο« 9 ο¨ 4 ο© ο« k ο½ 0
9
4 4 9 y ο 36 ο½ ο4 x ο« 24 60 ο« k ο½ 0
4 k ο½ ο60
required m ο½ ο 4 x ο« 9 y ο 60 ο½ 0
9 ο 4 x ο« 9 y ο 60 ο½ 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*
