11 x1 t05 06 line through pt of intersection (2013)
1. Equation of a line through a
point and intersection of
another two lines
2. Equation of a line through a
point and intersection of
another two lines
e.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).
3. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0
3x 5 y 9 0
4. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5
3x 5 y 9 0 3x 5 y 9
5. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
6. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
7. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2
8. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2 2 2 y 1 0
y3
9. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2 2 2 y 1 0
y3
the lines intersect at 2,3
10. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2 2 2 y 1 0
y3
3 2 the lines intersect at 2,3
m
2 1
1
3
11. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2 2 2 y 1 0
y3
3 2 1
y 2 x 1 the lines intersect at 2,3
m
2 1 3
1
3
12. Equation of a line through a
point and intersection of
another two lines
e.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).
2x y 1 0 10 x 5 y 5 ()
3x 5 y 9 0 3x 5 y 9
7x = 14
x 2 2 2 y 1 0
y3
3 2 1
y 2 x 1 the lines intersect at 2,3
m
2 1 3
1 3y 6 x 1
3 x 3y 7 0