11x1 t06 06 line through pt of intersection

Equation of a line through a point and intersection of

another two lines

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).

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).

2 1 03 5 9 0

x yx y

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x 2 2 1 0y

3y

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x 2 2 1 0y

3y the lines intersect at 2,3

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x 2 2 1 0y

3y the lines intersect at 2,3 3 2

2 113

m

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x 2 2 1 0y

3y the lines intersect at 2,3 3 2

2 113

m

12 13

y x

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).

2 1 03 5 9 0

x yx y

10 5 5

3 5 9x yx y

( )

7 = 14x 2x 2 2 1 0y

3y the lines intersect at 2,3 3 2

2 113

m

12 13

y x

3 6 13 7 0

y xx y

Alternatively

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

52 1 3 5 9 04

x y x y

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

52 1 3 5 9 04

x y x y

8 4 4 15 25 45 0x y x y

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

52 1 3 5 9 04

x y x y

8 4 4 15 25 45 0x y x y

7 21 49 0x y

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

52 1 3 5 9 04

x y x y

8 4 4 15 25 45 0x y x y

7 21 49 0x y 3 7 0x y

Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c

2 1 3 5 9 0x y k x y

1,2 : 2 1 2 1 3 1 5 2 9 0k

5 4 0k

4 554

k

k

52 1 3 5 9 04

x y x y

8 4 4 15 25 45 0x y x y

7 21 49 0x y 3 7 0x y

Exercise 5F; 2b, 3b, 6b(i), 7ab (i, iii), 9, 10, 13*

Exercise 5G; 2 to 14 evens, 15*