Math-EXE S4 chapter 2

Equation of Straight Line EX1

1. In each of the following, find the equation of the straight line.

a) Passing through (− 5, 6) and (− 1, 5)

1
b) Passing through (− 5, 2) with slope 3

c) 𝑥-intercept = − 9 and passing through the point (− 2, 4)

m
d) Passing through (1, − 9) and (2, 4)
e) 𝑦-intercept = − 5 and the inclination of 135°
f) 𝑥-intercept = 6 and the inclination of 45°

2.

co
Find the equation of the straight line passing through (2, 1) and perpendicular to
the line 4𝑥 − 6𝑦 + 16 = 0 .
e.
ex
3. Find the equation of the straight line passing through (5, − 3) and perpendicular
to the line 3𝑥 − 𝑦 + 1 = 0 .
h-

4. Find the equation of the straight line passing through (4, − 2) and parallel to the
line 2𝑥 − 3𝑦 + 8 = 0 .
at

5. Find the equation of the straight line passing through (8, − 3) and parallel to the
line 𝑥 − 6𝑦 + 4 = 0 .
m

6. Find the number of intersectional point(s) of the following.

a) 𝐿1: 2𝑥 + 3𝑦 + 4 = 0, 𝐿2: 4𝑥 + 6𝑦 + 1 = 0
4
b) 𝐿1: 𝑥 + 9 =− 3
𝑦, 𝐿2: 6𝑥 = 13 − 8𝑦

c) 𝐿1: 3𝑥 − 9𝑦 − 4 = 0, 𝐿2: 2𝑥 + 6𝑦 + 7 = 0

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Math-EXE S4 chapter 2

c-intercept :
-

E
Equation of Straight Line EX1
y-intercept -E
:

1. In each of the following, find the equation of the straight line.

Ch Y1 She Y
Slope--E
a) Passing through (− 5, 6) and (− 1, 5)
x,
31
1
b) Passing through (− 5, 2) with slope 3
(- 9 0) a y C ]2
. ,
c) 𝑥-intercept = − 9 and passing through the point (− 2, 4)
2
34Y1

m
jz
d) Passing through (1, − 9) and (2, 4)
e) 𝑦-intercept = − 5 and the inclination of 135°
f) 𝑥-intercept = 6 and the inclination of 45°

2.

co
Find the equation of the straight line passing through (2, 1) and perpendicular to
the line 4𝑥 − 6𝑦 + 16 = 0 .
e.
ex
3. Find the equation of the straight line passing through (5, − 3) and perpendicular
to the line 3𝑥 − 𝑦 + 1 = 0 .
h-

4. Find the equation of the straight line passing through (4, − 2) and parallel to the
line 2𝑥 − 3𝑦 + 8 = 0 .
at

5. Find the equation of the straight line passing through (8, − 3) and parallel to the
line 𝑥 − 6𝑦 + 4 = 0 .
m

6. Find the number of intersectional point(s) of the following.

a) 𝐿1: 2𝑥 + 3𝑦 + 4 = 0, 𝐿2: 4𝑥 + 6𝑦 + 1 = 0
4
b) 𝐿1: 𝑥 + 9 =− 3
𝑦, 𝐿2: 6𝑥 = 13 − 8𝑦

c) 𝐿1: 3𝑥 − 9𝑦 − 4 = 0, 𝐿2: 2𝑥 + 6𝑦 + 7 = 0

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 z(t-(-5))
Slope :E 5)
1a 1b -

/C 4-0
y z =

Slope
. .
.

-
z ( 9)-

y -) + t
-

= =
4
+ 11
x
3y 0 7
- =

6 π(x ( 5))
-
0 =
E( -
( 9)-

y y
- -
- =

y
=
Ex +
y
=
+ p my + +6
4x -

7y+ 36
=
0

=
G +2
y
4y 29 0
+ =
x
-

Id .

Slope =

4-12)
1)
=

( 9) 13(x 1)
y
-
- = -

a
+ =
13x 13 -

y
=
13x 22
y
-

13x1 0
y 22
- - =

2. IyXm = .
3 = 3Xm) =
1 4. =
3 =
mu
mc =
3
z mu =
- my
=
=
E( 2) ( 3) 5(x 5) ( 2) =(x 4)
y 1 y
- -
-
= -
- -
= -

y
-

=
-
-

y
-
=

Ex 3+/ -

y
=
-
zx 5 3 - -

y
=
= E -
- 2

y
=
-

Ex -
2

y
-
=
-x - y
=
= 3 -

14
by 3y 2x
= -
x -
= -

(1+
3y+ 14 0 2x 3y 2 0
=
- - =

5
. mc = 6a
Slope of 4 : 6b Stope of 4 = 3
: =
·
.

mi
=
t Slope of 12 t
:
-
= -
Slope of 12 =
= =
34
y ( 3) = j(x) 8) : The slopeare the same
they are parallel :
The
slope are the same they
- -

,
an
,

-x E intersection
yz O
point parallel
-
=
:
+

= 5) + > 0 insection point

y
2+ 26
by
=

x by + 26 0
-
=

62 .
Slope of1 :-
5 t =

2
of 5 -5
Slope
: - =

: There have I intersection point

 Math-EXE S4 chapter 2

7. In each of the following, find the equation of the straight line L.

a) b)

2 -
8
slope
=

0-CH)
E 4
yes
=
=
x

14
-
0) z= =( 0) -

y
-
,

= =x + 2
y
Ex y + z- = 0

m
zy 4
+ = 0
x -

co
c) d)

6
y
=
e.
Slope
=

800
(0 ,0)
8
ex
=
-

=
E
h-

y
-
0 =
&(x 0) -

y Ex
=
at

1
8. If the slope of the straight line 𝐿: 3𝑥 + 𝑏𝑦 − 18 = 0 is − 2
, find
a .

- - =
b. y- intercept
:
--
a) the value of 𝑏,
m

b 6
3
=
/ =

b) the 𝑦-intercept of 𝐿.

17
9. In each of the following, find the coordinates of the intersection of the two
straight lines 𝐿1 and 𝐿2.
an

a) 𝐿1: 2𝑥 + 𝑦 − 1 = 0, 𝐿2: 𝑥 − 𝑦 + 7 = 0

b) 𝐿1: 𝑦 =− 4𝑥 + 4, 𝐿2: 3𝑥 − 4𝑦 − 22 = 0

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Math-EXE S4 chapter 2

(0 ,
y) (340)
10. It is given a line 𝐿: 7𝑥 − 24𝑦 − 168 = 0. It cuts the 𝑥-axis at 𝐴 and the 𝑦-axis
at 𝐵. 𝑂 is the origin.

a) Find the coordinates of 𝐴 and 𝐵.

b) Find the circumference of ∆𝐴𝑂𝐵.
c) Find the area of ∆𝐴𝑂𝐵.

11. If 𝑃 is the intersection of the straight lines 𝐿1: 𝑦 =− 2𝑥, 𝐿2: 6𝑥 − 2𝑦 =− 30. 𝐿2

m
cuts the 𝑥-axis at 𝑄. 𝑂 is the origin.
(x 0)
,

a) Find the coordinates of 𝑃 and 𝑄.

co
I
b) Find the area of ∆𝑂𝑃𝑄.

(0 , 2)
12.
e.
The line 𝐿1: 4𝑥 + 2𝑦 – 4 = 0 intersects the 𝑦-axis at point 𝐴. Line 𝐿2 intersects

the 𝑥-axis at 𝐵(− 4 , 0). It is known that 𝐿1 and 𝐿2 do not intersect.

ex
Y
a) Find the coordinates of 𝐴 and the slope of 𝐿1.
parallel
b) Find the equation for 𝐿2, express the answer in general form.
h-

c) Find the equation for the horizontal line through the midpoint of 𝐴𝐵.

syy) i y
at

13. Line 𝐿 passes through 𝐴(3, 8) and 𝐵(− 9, − 2).

a) Find the equation for 𝐿, express the answer in general form.

b) Are 𝐴, 𝐵 and𝐶(7, − 2) collinear?
m

14. The slope of line 𝐿1 is − 2. Line 𝐿2 passes through 𝑀(4 , 3) and 𝐿1 ⊥ 𝐿2.

a) Find the equation for 𝐿2, express the answer in general form.

b) If 𝐿2 passes through 𝑁(𝑛 , 8), find the equation of the vertical line passing

through 𝑁.

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10a LetCl ,
0 =
Let =0
y
.

168 Ex 24(0) 168 0

710) 24y 0
- -
=
- = -

7 2 =
24
y
= -

The coordinates of A and B is (24 0) and 10 , -7) ,

respectively
b . AB2 72 +24- (pythotheorem)
=

=
25

circumference of AAOB is (7 + 25+ 24)

= 56
,

O .

119 Let -z into 22 Let

=
p
y
=

y
.

6x -
2) 2)
- = -

30 6) 2(0)
- = -

30
10x = -

30 x
=
5
x= 3
Th
-

(-3 6)
.

Let <1 = -
3 into 11
1)
2) 3) -

P
y
=
-

TheOrdinates of 4 is (3 , 6) and Qis ( - 5 1 0) * >

↓
y
X

5
Q
Ilb :

( 5 ,0)
-

Da
y
= --
4 = 2 Coordinates of A 10 , 2) :

Slope of 2
= -
E =
-2

12b of 2
Slope 2n = -

y
-
0 = -

2(x) -
( -

4))

2x 8
y
= - -

+8
2xL +
y 0
=

12c. Mid point of AB : (0 +4) It ,

= (-2 , 1)

y = 1
-
13a Slope :
.

-78 =

>
8
y =(x 3)
- =
-

y
=
=x - E +
y
=
Ex -
dy 5x 63
-
=

63 0
5x
by
-
- =

Bb of B2 (2)
Slope
-z -

0
.
= =

7 -

( 9)
-

Slope of AB :
5
·: Slope of AB Scope of R(

not collinear
They are

Har-2 x mrz =
-1
MLz =z

y
-
3 =
z(x 4) -

Ex + 1
y
=

+z
=
0
x
zy
-

I Let = 8 x n =

y
-

=
n -
2 (2) +2
n
= 14

The coordinate of I (14 , 8)

x = 14,
Math-EXE S4 chapter 2

Answers:

1. a) 𝑥 + 4𝑦 − 19 = 0 b) 𝑥 − 3𝑦 + 11 = 0
c) 4𝑥 − 7𝑦 + 36 = 0 d) 13𝑥 − 𝑦 − 22 = 0
e) 𝑥+𝑦+5=0 f) 𝑥−𝑦−6=0

2. 3𝑥 + 2𝑦 − 8 = 0

3. 𝑥 + 3𝑦 + 14 = 0

4. 2𝑥 − 3𝑦 − 14 = 0

m
5. 𝑥 − 6𝑦 − 26 = 0

6. a) 0 b) 0

co
c) 1

7. a) 𝑥 − 2𝑦 + 4 = 0 b) 𝑥=4
c) 𝑦=6 d) 4𝑥 − 3𝑦 = 0
e.
8. a) 6 b) 3
ex
9. a) (− 2, 5) b) (2, − 4)

10. a) 𝐴 (24, 0), 𝐵(0, − 7) b) 56 units

c) 84 sq.units
h-

11. a) 𝑃 (− 3, 6), 𝑄 (− 5, 0) b) 15 sq.units

at

12. a) 𝐴(0, 2), − 2 b) 2𝑥 + 𝑦 + 8 = 0

c) 𝑦=1

13. a) 5𝑥 − 6𝑦 + 33 = 0 b) no
m

14. a) 𝑥 − 2𝑦 + 2 = 0 b) 𝑥 = 14

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