11 x1 t05 04 point slope formula (2013)

Point Slope Formula

Point Slope Formula 1 1y y m x x

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6)

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

OR

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

OR 3 4 0x y k

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

OR 3 4 0x y k

2, 3 : 3 2 4 3 0k

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

OR 3 4 0x y k

2, 3 : 3 2 4 3 0k

6 06

kk

Point Slope Formula 1 1y y m x x

e.g. (i) Find the equation of the line passing through (–3,4) and (2,–6) 4 63 2

1052

m

4 2 3y x 4 2 6

2 2 0y x

x y

(ii) Find the equation of the line passing through (2,–3) and is parallel to 3x + 4y – 5 =0

3 54 4

y x

3required 4

m

33 24

y x

4 12 3 63 4 6 0y xx y

OR 3 4 0x y k

2, 3 : 3 2 4 3 0k

6 06

kk

3 4 6 0x y

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

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

9 64 4

y x

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

9 64 4

y x

4required 9

m

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

9 64 4

y x

4required 9

m

44 69

y x

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

To prove three lines (l, m, n) are concurrent;

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

To prove three lines (l, m, n) are concurrent;

( ) solve and simultaneouslyi l m

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

To prove three lines (l, m, n) are concurrent;

( ) solve and simultaneouslyi l m

( ) substitute point of intersection intoii n

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

To prove three lines (l, m, n) are concurrent;

( ) solve and simultaneouslyi l m

( ) substitute point of intersection intoii n

( ) if it satisfies the equation, then the lines are concurrentiii

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

9 64 4

y x

4required 9

m

44 69

y x

9 36 4 244 9 60 0y xx y

OR 4 9 0x y k

6,4 : 4 6 9 4 0k

60 060

kk

4 9 60 0x y

To prove three lines (l, m, n) are concurrent;

( ) solve and simultaneouslyi l m

( ) substitute point of intersection intoii n

( ) if it satisfies the equation, then the lines are concurrentiii

Exercise 5D; 1e, 2c, 4abc (i), 5b, 7d, 9, 11, 13, 15, 17ab (i),18ab (ii), 19, 22, 23c, 26*