Straight Line

ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1.

In the diagram , PQ is a straight line. y

P 4

2

– 4 – 3 – 2 – 1 0

1

2 x

– 2 Q

Find (a) the y-intercept, (b) the gradient , of the 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 3.

Determine the gradient of the straight line y = −

Answer :a)……………………… b)………………………

x +9 4 Answer :…………………

4. y F E(-2,6)

5.

0 G Determine the y-intercept of the straight line 2y – The diagram shows two straight lines, EF and FG, onx a=Cartesian plane. The gradient of EF is 1 and the distance of FG is 10 units. The x-intercept of FG is 38 Answer :………………………….

ppr maths nbk 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 -4

x 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

5 The diagram shows a parallelogram OPQR. Given that the gradient of OP = - . 3 The x-intercept of line QR is …......

Answer :……………………… 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)………………….

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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 2 line BD is parallel with the y-axis and the equation of line AB is y = x + 4. 3 y

B(6,10)

A

0 Find (a) the x-intercept of the straight line AB, (b) the gradient of AD,

C

D

x

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)……………………

1 8. In the diagram OM = OA and the length of the straight line OA is 9 units. 3 y A

B

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

x Answer a).................................. b)..................................

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9. In the diagram, CD is parallel to EF. y D y = 3x+5 0

C Find (a) the x-intercept of line CD, (b) the equation of straight line EF.

F x

E(-1,-4)

Answer: a)…………………… b)……………………

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

5 . Find 2

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.

M

y

6 x

8

0

Diagram 1 N

Find the gradient of MN. A -2 3 B 4 3 C 4 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. y

⋅

⋅

B

O

⋅

C

A(10,6) Diagram 2 x

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

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D

-3 y

⋅

⋅

P(8,2)

O

x Diagram 3

R(-2,-8) 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 3 5. In Diagram 4, the equation of the line WZ is y = x. 4 Q (8, k) is a point on the line WZ. y

⋅ Q (8, k) W

0

Diagram 4 x

Z 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 2 the line y = x + 5 is 3 2 A y= x+8 3 B 3y = 2x + 10 C 3y = 2x + 30 2 D y = x -3 3 46

ppr maths nbk

y E Diagram 5

G

0

x

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

⋅

y

U(-3,6)

Diagram 6

0

x

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 3 A 4 1 B 2 3 C 4 1 D 2

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y

⋅

R

0

⋅

J ( 4, 8 ) Diagram 7

⋅

P

x

10. In Diagram 7, the length of OP is 10 units. The equation of line PR is 4 A y= x+8 5 4 B y=- x+8 5 5 C y = x +4 4 5 D y=- x+4 4

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ppr maths nbk 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) b) c)

gradient of the line PQ , equation of the line RS , 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) b) c)

gradient of the line KL , equation of the line MN , y-intercept of the line MN.

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3.

y

F(3,k)

G(7,10)

E

O

x

H

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) b) c)

State the value of k , Find the equation of the line GH , 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) b) c)

State the coordinates of the point L , Find the y-intercept of the line KL, Find the equation of the line KL.

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5. y

V(8, k) U T(-2,1) x S

O Diagram 5

W

In Diagram 5 , the equation of the straight line STUV is 2y = x + 4. The lines OT and UW are parallel. Find the a) b) c)

value of k , y-intercept of the line STUV , equation of the line UW .

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ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 2

y

1. B(-3,10)

C

A

O

x

Diagram 1 The equation of the straight line AB in Diagram 1 is y = 2 x + 16. 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.

Y U

Z (6,5)

C (-2,3) V

O D (8,-2) 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.

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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 P

3

X

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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ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE DIAGNOSTIC TEST

y 1. A B (6, 5) D O

C (6, 0) Diagram 1

x

In Diagram 1, A and D are located on the y-axis and ABCD is a parallelogram. 1 If the gradient of AB = - , 2 a) State the gradient of CD. b) Determine the coordinates of D. c) Find the equation of the straight line AB. [ 5 marks ] 2. P (0, 9) Q (5, 7)

x

O R (0, -5) Diagram 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 ]

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y 3. M

P

O

x

N Diagram 3

4.

In Diagram 3, MN = 12 units and parallel to the y-axis. Given NO = 6 units and 2 PO = MN, 3 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 ] y D y = 2x + k A

O

x

E B

C Diagram 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]

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ppr maths nbk

5.

y P (-3, 6)

Q (h, k) M (4, 3) R

O

x

Diagram 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]

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