(107186844) f4-05-the-straight-line

8/13/2019 (107186844) f4-05-the-straight-line

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ppr maths nbk

EXERCISE 1

CHAPTER 5 : THE STRAIGHT LINE

1. In the diagram , PQ is a straight line.

P

y

4

2

4 3 2 1

0

1 2

x

2

Find

(a) the y-intercept,(b) the gradient ,

of the straight line.

2.y Q (5,1)

! P

" #

Q

$ns%er &a)''''''''.'.

b)'''''''''

etermine the y-intercept of the straight line 2y # * -

!

Find

a) the gradient of PQ

b) the e+ation of straight line PQ $ns%er &a)'''''''''

b)'''''''''

!. etermine the gradient of the straight line y *

x

+


2/23

ppr maths nbk

$ns%er &'''''''.

y

F

/(-2,0)

"

5.he diagram sho%s t%o straight lines, /F and F, on a 3artesian plane. he gradient of /Fis 1 and the distance of F is 1" nits. he #-intercept of F is

$ns%er &''''''''''.


3/23

0. he gradient of the straight line 2# 4 0y * 1!

$ns%er &'''''''''...

. he # - intercept of the straight line # 2y * 12 is

. In the diagram, $6 is a straight line.

$ns%er &'''''''''

y

$ -12

" #

-!

6

7hat is the gradient of $6 8

. In the diagram, 9: * 9;. he e+ation of :; is

y

;

: #

- "

1". In the diagram ,


4/23

EXERCISE 2


1. y

P Q (!,5)

9 : #

he diagram sho%s a parallelogram 9PQ:. i>en that the gradient of 9P * -

5

.!

he #-intercept of line Q: is '......

$ns%er &'''''''''

2.

y

Q(",5)

:(12,!)

P" #

;(,?)

In the diagram, PQ:; is a parallelogram. he e+ation of the straight line :; is

2y * # 0. Find

a) the >ale of ?,

b) the gradient of the straight line Q:,$ns%er& a)''''''''

b)'''''''.


5/23

!. In the diagram, 9PQ: is a parallelogram and 9 is the origin.

Find

a) the gradient of the straight line 9:,b) the e+ation of the straight line PQ

y Q

:(2,)

P(0,1)

" #$ns%er& a)'''''''

b)'''''''.

. In the diagram PQ:; is a parallelogram

P(-2,12) y

Q

; " #

a) i>en that the gradient of line PQ is -!,

find the e+ation of PQ

b) Find the coordinate of point :.

:

$ns%er a).................................

b) ................................


6/23


7/23

y

Q(,)

;(1",2)

" P(2,") : #

. In the diagram, PQ is parallel to :; and 9 is the origin.

Finda) the gradient of :;

b) the #- intercept of :;

$ns%er& a)''''''''

b)''''''''

. In the diagram 9< *

1

9$ and the length of the straight line 9$ is nits.!

y

$ 6

" < #(a) Find the coordinate of point 6.

(b) 3alclate the gradient of line


8/23


9/23

DIAGNOSTIC TEST


1. In iagram 1,


10/23

$ !6 3

he gradient of line 63 is


11/23

-!

y

P(,2)

9

:(-2,-)

#

iagram !

. 6ased on iagram !, find the e+ation of line P:.

$ y * -# 0

6 y * -# 4 03 y * # 4 0

y * # 05. In iagram , the e+ation of the line 7B is y *

Q (, ?) is a point on the line 7B.

y

!

#.

7

Q (, ?)iagram

" #

B

Find the >ale of ?.$ 06

3

0. he e+ation of a straight line passing throgh the point ( -!, ) and parallel to

the line y *2

# 4 5 is!

$ y *2

# 4 !6 !y * 2# 4 1"

3 !y * 2# 4 !"

y *2

# -!!


12/23

y

/

iagram 5

" #

. In iagram 5, 9/ * 9. Find the gradient of line /.

$ 16 -1

3 2

-2

y

C(-!,0)

iagram 0

#"

. In iagram 0, find the gradient of the line 9C.$ 16

3 2

. he y-intercept of the straight line y * ! 2# is

$

!

6 -

12

3 -

!

12


13/23

y

:

D ( , )

iagram

#" P

1". In iagram , the length of 9P is 1" nits. he e+ation of line P: is

$ y *

# 4 5

6 y * -

# 4 5

3 y *5

# 4

y * -

5

# 4


14/23


EXERCISE 1

1. y :(5,)

Q(1,)

#

P(-1,") 9

;iagram 1

In iagram 1, straight lines PQ and :; are parallel. Find the

a) gradient of the line PQ ,

b) e+ation of the line :; ,

c) #-intercept of the line :;.

2. y.A

E #

9


15/23

!. y F(!,?) (,1")

/

9 @#

iagram !In iagram !, straight line F is parallel to the #-a#is %hile the lines /F and @ are

parallel. he gradient of the line /F is 2.

a) ;tate the >ale of ? ,

b) Find the e+ation of the line @ ,

c) Find the coordinates of the point / .

. y

< (5,2")

=9 #

E

iagram

In iagram , 9E=< is a parallelogram and line


16/23

5.

y

(, ?)

C

(-2,1)#

; 9 7

iagram 5

In iagram 5 , the e+ation of the straight line ;C is 2y * # 4 . he lines 9 and

C7 are parallel. Find the

a) >ale of ? ,

b) y-intercept of the line ;C ,

c) e+ation of the line C7 .


17/23

EXERCISE 2

1.


y

6(-!,1") 3

#$ O

iagram 1

he e+ation of the straight line $6 in iagram 1 is

a) ;tate the e+ation of the straight line 63,

b) Find the #-intercept of the straight line $6,c) Find the e+ation of $3.

y = 2x +10.

G

C

B (0,5)

3 (-2,!)

O

(,-2)

2.

iagram 2

In iagram 2, the straight line C is parallel to 3. 9 is the origin.

a) 3alclate the gradient of line 3,

b) Find the e+ation of line CB,

c) Find x- intercept of line CB.


18/23

!. y

:

Q (h , ! )

#

P( -, " ) " ; ( 0, " )

iagram !

In iagram !, the gradient of the straight line PQ: is !.Find the

a) >ale of h

b) y-intercept of the line :;

c) e+ation of the line :;

. y

6 (2 , )

3

$ (2 , ! )

#

"

iagram

In iagram , 9$63 is a parallelogram. Find the

a) coordinates of 3

b) e+ation of the straight line 63


19/23

5.

G

Q ;

12

- ! H

P :

iagram 5

In iagram 5, straight lines PQ and :; are parallel.

a) ;tate the gradient of PQ

b) Find the e+ation of :;

c) Find the intercept of :;


20/23


DIAGNOSTIC TEST

y

1.

$

6 (0, 5)

93 (0, ")

#

iagram 1

In iagram 1, $ and are located on the y-a#is and $63 is a parallelogram.

If the gradient of $6 * -

1

,2

a) ;tate the gradient of 3.

b) etermine the coordinates of .

c) Find the e+ation of the straight line $6.

5 marks J

2.

P (", )

Q (5, )

9#

: (", -5)

iagram 2iagram 2 sho%s a triangle PQ:.

a) ;tate the y-intercept of the straight line PQ,

b) Find the e+ation of the straight line Q:,

c) Find the e+ation of a straight line that passes throgh P and parallel to the straight

line Q:. 5 marks J


21/23

y!.

en 9 is the

origin. Find

a) the >ale of h and ?,

b) the e+ation of the straight line P: .

5 marksJ

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(107186844) f4-05-the-straight-line