straight line 1

7/29/2019 Straight Line 1

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CHAPTER 12: THE STRAIGHT LINE

GRADIENT m =2 1

2 1

y y

x x

Example Exercises

1) (1,2) and (3,4) 1.) ( 2,1) and (4,3)

m =13

24

=2

2= 1

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2) (-1,2) and (3,4) 2.) (- 2,1) and (4,3)

m=)1(3

24

=4

2=2

1

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3) (1,-2) and (3,4) 4.) (2,-1) and (4,3)

------------------------------------------------------------------------------------------------------------

5) (-1,-2) and (3,4) 6.) (-2,-1) and (4,3)

------------------------------------------------------------------------------------------------------------

7) (-1,-2) and (-3,-4) 8.) (-2,-1) and (-4,-3)

------------------------------------------------------------------------------------------------------------

9) (0,2

1) and ( 0,

2

3) 10) (-

2

1,2

3) and (

2

1,-2

1)

INTERCEPT

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X-intercept y = 0

Example Exercise

1) 42 += xy 1) 63 += xy

4200 +== xy

22

4

42

24

=

=

=

=

x

x

x

x- intercept = -2

---------------------------------------------------------------------------------------------------------------------

2) 25 = xy 2) 52 += xy

2500 == xy

5

2

25

52

=

=

=

x

x

x

x-intercept =2

5

---------------------------------------------------------------------------------------------------------------------

3) 54 += xy 4.) 13 += xy

---------------------------------------------------------------------------------------------------------------------

5) 632 = xy 6) 522 += xy

7) 63

2+= xy 8) 4

5

2= xy

The Straight Line 2

y-intercept (x = 0)

X-intercept (y = 0)


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9) 125

32 += xy 10) 3

9

13 = xy

--------------------------------------------------------------------------------------------------------------------

11) 122 += xy 12) 233 = xy

y intercept x = 0

Example Exersice

1) 62 += xy 1) 83 += xy

x = 0 , y = 2(0) + 6

y = 6y- intercept = 6

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2) 72 = xy 3) 93 = xy

---------------------------------------------------------------------------------------------------------------------

4) 63

2+= xy 5) 6

2

1= xy

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---------------------------------------------------------------------------------------------------------------------

6) 73

2+= xy 7) 10

5

2= xy

---------------------------------------------------------------------------------------------------------------------

Example

8) 125

32 += xy 9) 21

9

13 = xy

X = 0, 2y =5

3(0) + 12

2y = 12

y = 6

y intercept = 6--------------------------------------------------------------------------------------------------------------------

10) 122 += xy 11) 233 = xy

..

PAST YEARS SPM QUESTIONS

1 SPM 2003

The gradient of the straight line

2x-7y =14 is

A 6 6B

The Straight Line 4


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C 3 3

2 2D

A 2

7

4 SPM 2004

B 7

2

C -2

D 7

2 2004J

Diagram below shows a straight line

MN on a Cartesian plane.

The gradient of MN is

The gradient of QR is -4 and the distance of

PQ is 15 units,

Find the x-intercept of PQ

A -9

B -12

C 9

4

D 15

4

A 5

12

5 SPM 2004

Diagram below shows a straight line LM on

a Cartesian plane.

B 6

11

C 2

9

D 3

8

3 2004 J

The graph in the diagram below shows

a straight line JK with gradient1

2

Calculate the x-intercept of JK

The gradient of LM

A -1

B-1

2

C 1

2

D 1

The Straight Line 5

R(1,8)

P0

y

x

Q

N(0,4)

M(-2, -1)

0

y

x

J(0,3)

K

0

y

x


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6 The gradient of the straight line

24 8

3y x is =

9 SPM 2005

In the diagram below, PQ is a straight line.

A 1

6

B 8

3

C 2

D 6

7 Diagram below shows a straight line

RS which has gradient4

3

The y-intercept of RS is

What is the gradient of PQ?

A -2

B 1

2

C 12

D 2

10 SPM 2006 J

State the y-intercept of the straight line 3y-

2x-11=0

A 11

3

B 11

3

C 11

2

A 4 D 11

2

B 9

C 12

D 16 11 The straight line PQ has gradient of 2. The

coordinates of P are (0,6).

The x-intercept of PQ is

8 SPM 2005 A -3

Find the y-intercept of the straight line

3x-4y=24 B1

3

A 3

4

C 1

3

B 4

3

D 3

C -6

D 8

The Straight Line 6

S

R(-12,0) x

y

0


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12. SPM 2006 (N)

The coordinates of point P(-1,1) and the

gradient of the straight line PQ is 2.

The coordinates of point Q could be

A (3,3)B (3,9)

C (3,-1)D (3, -7)

13. SPM 2006(N)

In Diagram below, EF is a straight line with

gradient1

4

Find the x-intercept of the straight line EF.

A 1

12

B 3

4

C -3

D -12

SPM 2007(J)

14. In Diagram 16, PQR is a straight line

and O is the origin.

A.3

5

B.5

3

C.

5

3

D.3

5

15. A straight line has a gradient7

3and

passes through the point (0,6). The

x- intercept of the straight line is

A. -14

B. -6

C. 6

D. 14

16. SPM 2008(J)Diagram 15 shows a straight line KL,

on a Cartesian plane

The gradient of KL is2

3. Find the

Value of h

A. 3

11

B. 3

13

C. 7

D. 11

17. Find the y-intercept of the straight line

The Straight Line 7

x

y

E

F

-3

0

y

x

P

R(3,-5)

Diagram 16

O x

L(6,h)

K(-2,-1)

K(-2,-1)

y

Diagram 15


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5y = 3x 6

A. -6

B.5

6

C. 5

3

D. 3

SPM 2008(N)

18.Diagram 16 shows a straight line PQ on

a Cartesian plane.

Find the gradient of PQ.

A. 3

B. 2

C. 2

1

D. 3

1

19. State the x-intercept of the straight line

3x 4y + 24 = 0

A. -8

B. -6

C. 6

D. 8

The Straight Line 8

O x

Q(5,4)

P(-1,2)

y

Diagram 16


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ANSWERS

Chapter 12 I The Straight Line

1. A

2. A

3. A4. A

5. B

6. A7. D

8. C

9. D

10. B11. A

12. B

13. D

14. D15. D

16. D17. B

18. D

19. A

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straight line 1

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