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CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1. In the diagram , PQ is a straight line.

Answer :a)…………………….…. b)……………………… 2. y Q (5,18) 3 P 0 x

Find

a) the gradient of PQ b) the equation of straight line PQ Answer :a)……………………… b)………………………

3. Determine the gradient of the straight line y = 94+−

x

Answer :…………………

4. y F E(-2,6) 0 G 5. Determine the y-intercept of the straight line 2y – x = -

Find (a) the y-intercept, (b) the gradient , of the straight line.

The diagram shows two straight lines, EF and FG, on a Cartesian plane. The gradient of EF is 1 and the distance of FG is 10 units. The x-intercept of FG is

Answer :………………………….

y

x1 2 – 1 – 2 – 3 – 4

2

4

– 2

P

Q

0

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6. The gradient of the straight line 2x + 6y = 13 Answer :………………………... 7. The x - intercept of the straight line 4x – 2y = 12 is

Answer :……………………… 8. In the diagram, AB is a straight line. y A -12 0 x -3 B What is the gradient of AB ?

Answer :……………………….. 9. In the diagram, OR = OS. The equation of RS is y S R x -4 0 Answer:………………………… 10. In the diagram , MLT is a right-angled triangle. . y L(6,7) M T(6,4)

0 x

Find a) the coordinate of M, b) the equation of the straight line LT.

Answer :.a)…............................. b)…………………….

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CHAPTER 5 : THE STRAIGHT LINE

EXERCISE 2 1. y P Q (3,5) O R x 2. y

Q(0,5)

R(12,3)

P 0 x S(4,k) In the diagram, PQRS is a parallelogram. The equation of the straight line RS is 2y = x – 6. Find a) the value of k, b) the gradient of the straight line QR,

Answer: a)…………………… b)………………….

The diagram shows a parallelogram OPQR. Given that the gradient of OP = -35 .

The x-intercept of line QR is …...... Answer :………………………

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3. In the diagram, OPQR is a parallelogram and O is the origin. Find a) the gradient of the straight line OR, b) the equation of the straight line PQ y Q R(2,4) P(6,1) 0 x Answer: a)………………… b)…………………. 4. In the diagram PQRS is a parallelogram P(-2,12) y Q S 0 x R a) Given that the gradient of line PQ is -3, find the equation of PQ b) Find the coordinate of point R. Answer a)................................. b) ................................

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5. In the diagram, LH is a straight line. Given that the gradient of the straight line LH is -1. y L(-3,9) H(0,k) 0 x Find (a) the value of k, (b) the equation of the stragiht line LH.

Answer: a)…………………… b)……………………. 6. In the diagram above, ABCD is a parallelogram and O is the origin. The straight

line BD is parallel with the y-axis and the equation of line AB is y = 32 x + 4.

y B(6,10) A C 0 D x Find (a) the x-intercept of the straight line AB, (b) the gradient of AD,

Answer: a)…………………… b)……………………

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y Q(4,8) S(10,2) 0 P(2,0) R x

7. In the diagram, PQ is parallel to RS and O is the origin. Find a) the gradient of RS b) the x- intercept of RS

Answer: a)……………………

b)……………………

8. In the diagram OM =31 OA and the length of the straight line OA is 9 units.

y

A B

0 M x (a) Find the coordinate of point B. (b) Calculate the gradient of line MB. Answer a).................................. b)..................................

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9. In the diagram, CD is parallel to EF. y D y = 3x+5 F 0 x C Find E(-1,-4) (a) the x-intercept of line CD, (b) the equation of straight line EF.

Answer: a)…………………… b)……………………

10. In the diagram, EFGH is a parallelogram. Given that the gradient of line EF is 25 . Find

the coordinate of point G. y E H(8,5) . F 0 G x

Answer: ……………………

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CHAPTER 5 : THE STRAIGHT LINE DIAGNOSTIC TEST

1. In Diagram 1, MN is a straight line.

Find the gradient of MN.

A -2

B 43

C - 43

D 2

2. Given that the equation of a straight line is x – 2y + 3 = 0. Find the x-intercept of the straight line. A -1 B -2 C -3 D -4 3. In Diagram 2, the length of OC is 2 units.

The gradient of line BC is A 3 B 4 C -4

y

O x

C

B A(10,6) ⋅⋅

⋅Diagram 2

N

M

8

6

0

y

x Diagram 1

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D -3

4. Based on Diagram 3, find the equation of line PR. A y = -x – 6 B y = -x + 6 C y = x + 6 D y = x – 6

5. In Diagram 4, the equation of the line WZ is y = 43 x.

Q (8, k) is a point on the line WZ.

Find the value of k. A 6 B 7 C 8 D 9

6. The equation of a straight line passing through the point ( -3, 8 ) and parallel to

the line y = 32 x + 5 is

A y = 32 x + 8

B 3y = 2x + 10 C 3y = 2x + 30

D y = 32 x -3

0

y

Z x

Q (8, k)

W⋅

Diagram 4

O

P(8,2)

R(-2,-8)

y

⋅

⋅x

Diagram 3

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7. In Diagram 5, OE = OG. Find the gradient of line EG. A 1 B -1 C 2 D -2

8. In Diagram 6, find the gradient of the line OU. A 1 B -1 C 2 D -2 9. The y-intercept of the straight line 4y = 3 – 2x is

A 43

B -21

C -43

D 21

G

E

x

y

0

Diagram 5

0

y U(-3,6)

x

⋅Diagram 6

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10. In Diagram 7, the length of OP is 10 units. The equation of line PR is

A y = 54 x + 8

B y = -54 x + 8

C y = 45 x +4

D y = -45 x + 4

P

R J ( 4, 8 )

0 x

y

⋅

⋅

⋅ Diagram 7

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CHAPTER 5 : THE STRAIGHT LINE

EXERCISE 1 1. y R(5,7) Q(1,4) x P(-1,0) O S Diagram 1 In Diagram 1, straight lines PQ and RS are parallel. Find the

a) gradient of the line PQ , b) equation of the line RS , c) x-intercept of the line RS.

2. y. N K x O M(5,0) L Diagram 2

In Diagram 2, straight lines KL and MN are parallel. The equation of the line KL is y + 3x + 3 = 0. Find the

a) gradient of the line KL , b) equation of the line MN , c) y-intercept of the line MN.

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3. y F(3,k) G(7,10) E x Diagram 3

In Diagram 3, straight line FG is parallel to the x-axis while the lines EF and GH are parallel. The gradient of the line EF is 2.

a) State the value of k , b) Find the equation of the line GH , c) Find the coordinates of the point E .

4. y M (5,20) L O x K Diagram 4 In Diagram 4, OKLM is a parallelogram and line ML is parallel to the y-axis.Point L is

on the x-axis.

a) State the coordinates of the point L , b) Find the y-intercept of the line KL, c) Find the equation of the line KL.

O H

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5. y V(8, k) U T(-2,1) x S O W Diagram 5 In Diagram 5 , the equation of the straight line STUV is 2y = x + 4. The lines OT and UW are parallel. Find the

a) value of k , b) y-intercept of the line STUV , c) equation of the line UW .

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CHAPTER 5 : THE STRAIGHT LINE EXERCISE 2 1. Diagram 1 The equation of the straight line AB in Diagram 1 is .162 += xy

a) State the equation of the straight line BC, b) Find the x-intercept of the straight line AB, c) Find the equation of AC.

2. Diagram 2 In Diagram 2, the straight line UV is parallel to CD. O is the origin.

a) Calculate the gradient of line CD, b) Find the equation of line UZV, c) Find x- intercept of line UZV.

Z (6,5)

Y U

V C (-2,3)

D (8,-2) O

B(-3,10)

A O

C

x

y

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3. y R Q (h , 3 ) x P( -8, 0 ) 0 S ( 6, 0 ) Diagram 3 In Diagram 3, the gradient of the straight line PQR is 3.Find the

a) value of h b) y-intercept of the line RS c) equation of the line RS

4. y B (2 , 8 ) C A (2 , 3 ) x 0 Diagram 4 In Diagram 4, OABC is a parallelogram. Find the

a) coordinates of C b) equation of the straight line BC

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5. Y Q S 12

-4 3 X P R Diagram 5 In Diagram 5, straight lines PQ and RS are parallel.

a) State the gradient of PQ b) Find the equation of RS c) Find the intercept of RS

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CHAPTER 5 : THE STRAIGHT LINE DIAGNOSTIC TEST 1. In Diagram 1, A and D are located on the y-axis and ABCD is a parallelogram.

If the gradient of AB = -21 ,

a) State the gradient of CD. b) Determine the coordinates of D. c) Find the equation of the straight line AB.

[ 5 marks ]

2. Diagram 2 shows a triangle PQR.

a) State the y-intercept of the straight line PQ, b) Find the equation of the straight line QR, c) Find the equation of a straight line that passes through P and parallel to the straight

line QR. [ 5 marks ]

Diagram 1

A B (6, 5)

C (6, 0)

D x

y

O

P (0, 9)

Q (5, 7)

O R (0, -5)

x

Diagram 2

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3. In Diagram 3, MN = 12 units and parallel to the y-axis. Given NO = 6 units and

PO = 32 MN,

a) State the coordinates of P, b) Find the gradient of the straight line PM, c) Find the equation of the straight line PM.

[ 5 marks ]

4. In Diagram 4 , two straight lines AB and CD intersect at point (-1, 3). Given the gradient of AB is -1, find the

a) value of k, b) equation of the straight line AB, c) coordinates of point E.

[ 5 marks]

A

B C

D

O x

y

M

N O

P

x

y

Diagram 3

y = 2x + k

Diagram 4

E

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5. In Diagram 5, OQ and PR intersect at M which is midpoint of OQ. Given O is the

origin. Find

a) the value of h and k, b) the equation of the straight line PR .

[ 5 marks]

y

Q (h, k)

M (4, 3)

P (-3, 6)

Ox

Diagram 5

R