A l 1 2 x 2 y 6 0 b l 1 4 x 6 y 0 c l 1 3 x 4 y 1 l 2

(a) L
1
: 2 x – 2 y – 6 = 0 (b) L
1
: 4 x – 6 y = 0 (c) L
1
: 3 x + 4 y = 1
L
2
: x – y – 3 = 0 L
2
: 9 x + 6 y – 1 = 0 (a) L
2
: 6 x + 8 y
Example 3.3 [
Book 4A 2.14
(a) Two straight lines L
1
: 8 x + ky –10 = 0 and L
2
: 4 x + 7 y + h = 0 have an infinite number of
intersections. Find the values of h and
(b) Do the two straight lines L
1
: 3 x + y + k = 0 and L
2
: kx – 2 y +12 = 0 have an infinite
number of intersections? Explain your answer.
= –1
]
k .
Daily Homework: Ex. 2C (13, 15, 16, 18, 20, 21, 24, 25, 26, 29)

40
40
Supplementary Exercise on Equations of Straight Lines (Optional)
1. It is given that the x -intercept and y -intercept of straight line L are 1 and 2 respectively.
(a) Find the equation of L . [2 x + y – 1 = 0]
(b) Does lie on L ? [Yes]
2. In the figure, straight lines L
1
: y = 2 x + k and L
2
intersect at P (1,3
(a) Find the value of k .
k ).
[1]
(b) If the x -intercept of L
2
is 5, find the equation of L
2
3. In the figure, straight lines L
1
and L
2
intersect at P (2 k ,2 k – 1). It is given that
the slope of L
2
is 2.
(a) Find the coordinates of P . [(–2, –3)]
(b) Find the equation of L
2
. [2 x – y + 1 = 0]
4. In the figure, straight lines L
1
: x + y – 2 b = 0 and L
2
: x = 3 intersect at A
(a) Find the coordinates of A . [(3, 3)]
(b) Find the equation of the straight line passing through the origin and A
( a , b ).
.
5. It is given that straight line L passes through A (1, –5). If the x -intercept of
twice its y -intercept, find the equation of L . [ x + 2 y + 9 = 0]
L is
6. Two points A (–5, 4) and B (–2, –2) are given. C is a point on AB produced such that AB : BC
(a) Find the coordinates of C . [(0, –6)]
(b) Find the equation of the straight line with the slope of 2 passing through C
= 3: 2.
.
7. It is given that straight line L : kx + (2 k – 3) y + 4 = 0 passes through P (2, –8) and cuts the x -axis and
axis at A and B respectively.
(a) Find the value of k .
y -
[2]
(b) Find the area of Δ OAB . [4 sq. units]
8. In the figure, straight line L
1
: 3 x – 2 y + 24 = 0 cuts the x -axis and y -axis at
A and B respectively. Straight line L
2
is the perpendicular bisector of line
segment AB and cuts the x -axis and y -axis at C and D respectively.
(a) Find the coordinates of A and
(b) Find the equation of L
2
. [2 x + 3 y – 10 = 0]
B .
(c) Find the area of ODMA . [ sq. units]
92
3
5
y
k
1
3
)
0
y
O
x
L
2
L
1
: 3 x - 2 y + 24 = 0
M
A
D
C
B

Set 2: Measure, Shape and Space Strand Equations of Straight Lines 41
Prepared by hkmathslearn
41
Example 4.1 [
Further Practice
]
In the figure, the straight line L
1
cuts the y -axis at A (0,4) and the
x -axis at B . The straight line L
2
cut the y -axis at C and has
slope 3. The straight line L
3
: y = x – 4 passes through B and
L
1
and L
2
intersect at D
(a) Find the x -intercept and the y -intercept of L
C .
.
3
.
(b) Find the equations of L
1
and L
2
(c) Find the area of Δ BCD .
Example 4.2 [
Further Practice
]
The figure shows three straight lines L
1
, L
2
and L
3
. L
1
passes
through A (–8,5) and B (–2,2). L
2
passes through (–5,6) and its
x -intercept is –3. L
3
is perpendicular to L
1
and passes through
the intersection P of L
1
and L
2
. Find
(a) the equations of L
1
, L
2
and L
.
3
.