modul 13 hukum linear 2
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MODUL 13 / TG5: HUKUM LINEAR
KERTAS 1
1. Ungkapkan persamaan ak !"near x# y $ m % nx# &a!am 'en(k Y %mX $c.)&engan kea&aan
m &an n a&a!a* pema!ar.
Express the non-linear equation x2 y + m = nx2 in the form of Y=mX+c. +*ere m an& n
are ,-nsans.
3 m / Aras R
#. Ungkapkan persamaan ak !"near Fakx % y &a!am 'en(k Y %mX $c. Ten(kan (ngkapan
'ag" Y, X, m, an& c, &engan kea&aan a, k &an F a&a!a* pema!ar .
Express the non-linear equation Fakx = y in the form of Y=mX+c. Determine the
expressions of Y, X, m, an c, !here a, k an F are constants.
3 m / Aras R
3. D"'er" q &an p &"*('(ngkan -!e* persamaan p=h$ &engan kea&aan h &an k
"a!a* pema!ar. Terangkan 'aga"mana n"!a" h &an k &apa &"per-!e*" &ar"pa&a sa(
gra0 gar"s !(r(s.
"i#en q an p are relate $y the equation p=h+!here h an k are constants.
Explain ho! the #alues of h an k can $e o$taine from a strai%ht line %raph.
3 m / Aras R
. Ra2a* 1 &" 'a+a* men(n2(kkan se'a*ag"an gra0 gar"s !(r(s ang &"!(k"s &engan
persamaan cx + y = xy &" mana c &an a&a!a* pema!ar.
Dia%ram & sho!s part of a strai%ht line %raph ra!n to represent equation
cx + y = xy !here c an are constants.
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
qk
q
qk
q
x
y
x
( 0, )
(4, 3)
0
13
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MODUL 13 / TG5: HUKUM LINEAR
Ra2a* 1 / Dia%ram &
4ar" n"!a" c &an .
Fin the numerical #alue of c an . m / Aras S
5. em'-!e* ('a* x &an y &"*('(ngkan -!e* persamaan y % kx)&engan kea&aan k a&a!a*
pema!ar.
'he #aria$les x an y are relate $y the equation y = kx( , !here k is a constant.
6a7 T(karkan persamaan y % kx kepa&a 'en(k !"near.
)on#ert the equation y = kx(
to linear form. # m / Aras S
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
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MODUL 13 / TG5: HUKUM LINEAR
6a7 Ra2a* # men(n2(kkan gar"s !(r(s ang &"per-!e* &engan memp!- !-g18 y
me!a+an !-g18 x.
Dia%ram 2 sho!s the strai%ht line o$taine $y plottin% lo% &* y a%ainst lo% &* x
4ar" n"!a"
Fin the #alue of6"7 !-g18 k )
6""7 h.
# m / Aras S
Ra2a* # / Dia%ram 2
.
9. em'-!e* ('a* x &an y &"*('(ngkan -!e* persamaan y % kx3 &engan kea&aan k a&a!a*
pema!ar.
'he #aria$les x an y are relate $y the equation , !here k is a constant.
6 a 7 4ar"kan *('(ngan anara &an ..
Fin the relationship $et!een an .
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
3 y kx=
18!-g y18!-g x
18!-g y18!-g x
!-g18
y
!-g18
x
• 6 8) 7
•
63) h 7
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MODUL 13 / TG5: HUKUM LINEAR
# m / Aras S
6 '7 Ra2a* 3 men(n2(kkan gar"s !(r(s ang &"per-!e* &engan memp!- !-g18 y
me!a+an !-g18 x.
Dia%ram sho!s the strai%ht line o$taine $y plottin% a%ainst lo% &* x.
4ar" n"!a" 'ag" Fin the #alue of
6"7 ,
6""7 h # m / Aras S
Ra2a* 3 / Dia%ram
. Ra2a* men(n2(kkan se'a*ag"an gra0 gar"s !(r(s ang &"per-!e*" &ar"pa&a
p!- me!a+an x#.
Dia%ram ( sho!s part of a strai%ht line %raph o$taine $y plottin% a%ainst
x2.
69)87 x#
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
18!-g y
18!-g k
x
y
x
y
x
y
68) #76) h7
•
•
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MODUL 13 / TG5: HUKUM LINEAR
68);37
Ra2a* / Dia%ram (
6a7 Ungkapkan &a!am se'(an
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MODUL 13 / TG5: HUKUM LINEAR
Ra2a* 5 / D"agram 5
4ar"/ Fin 6a7 !-g y &a!am se'(an !-g x
lo% y in terms of lo% x # m / Aras S
6'7 n"!a" y apa'"!a x % # m/ Aras S
#alue of y !hen x = (
>. Ra2a* 9 men(n2(kkan gra0 gar"s !(r(s ang &"*('(ngkan -!e* persamaan y % a x '
&engan kea&aan a &an $ "a!a* pema!ar.
Dia%ram / sho!s the %raph of the strai%ht line that is relate $y the equation
y = ax$ !here a an $ are constants.
!-g y
6)87 !-g x
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
•68);#7
•
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MODUL 13 / TG5: HUKUM LINEAR
D"agram 9
4ar")
Fin,
6a7 n"!a" a &an $ 3 m / Aras S
the #alue of a an $,6'7 n"!a" y apa'"!a x % 5 # m / Aras S
the #alue of y !hen x = .
18. Ra2a* men(n2(kkan gra0 gar"s !(r(s ang 'er*('(ng &engan persamaan
xy = ax2 + $ &engan kea&aan a &an $ "a!a* pema!ar.
Dia%ram 0 sho!s the %raph of the strai%ht line that is relate $y the equation
xy = ax2 + $ !here a an $ are constants.
xy 611)97
61)#7
x#
Ra2a* / Dia%ram 0
4ar" n"!a" a &an $.
Fin the #alue of a an $.
m / Aras S
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
•
•
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MODUL 13 / TG5: HUKUM LINEAR
11. Ra2a* = men(n2(kkan gra0 me!a+an .
Dia%ram 1 sho!s a linear %raph of a%ainst .
x#
Ra2a* = / D"agram =
em'-!e*('a* x &an y
&"*('(ngkan &engan
persamaan ) &engan kea&aan p
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
y
1# x
y
1# x
y
1
q x y
p+=
##
? 6 8 ) ;# 7
? 6 ) 9 7
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MODUL 13 / TG5: HUKUM LINEAR
&an q "a!a* pema!ar.
'he #aria$les an are relate
$y the equation , !here an are
constants)
6a7 en(kan n"!a" p &an @)
etermine the #alues of an , # m / Aras S
6'7 (ngkapkan &a!am se'(an x
express in terms of . # m / Aras S
1#. 4ar" persamaan 'ag" gar"s !(r(s pen(a"an er'a"k 'er&asarkan gra0 'er"k( &an
en(kan n"!a" x apa'"!a y % .5.
Fin the equation of the line of $est fit $ase of the follo!in% %raph an etermine
the #alue of x !hen y = (..
. m / Aras T
13 Ra2a* > men(n2(kkan gra0 !engk(ng y % – x# + 5 &an ra2a* 18 men(n2(kkan gra0 !"near
ang &"per-!e* apa'"!a y % – x2 + 5 &"(ngkapkan &a!am 'en(k !"near Y % 5 X + ,.
Ungkapkan X &an Y &a!am se'(an x &an/aa( y.
Dia%ram sho!s the cur#e y = – 0x2 + an ia%ram &* sho!s the linear %raph
o$taine !hen y = – 0x2 + is expresse in the linear form Y = X + c. Express X an Y
in terms of x an3or y. 3 m / Aras T
MODUL SOLAF MATEMATIK TAMBAHAN M13 -
x y
q p
q pq x
y
p+=
## y x
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MODUL 13 / TG5: HUKUM LINEAR
Ra2a* > / D"agram >
Ra2a* 18/ D"agram 18
1. Ungkapkan y &a!am se'(an x 'er&asarkan gra0 ang 'er"k(.
Express y in terms of x $ase on the follo!in% %raph. 3 m / Aras S
15. Ra2a* 'er"k( men(n2(kkan gra0 !"near
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MODUL 13 / TG5: HUKUM LINEAR
19 . em'-!e* ('a* x &an y &"*('(ngkan &engan persamaan y = pq x) &engan kea&aan p &an
q "a!a* pema!ar. B"ka gra0 !-g y me!a+an x &"p!-)sa( gar"s !(r(s &engan ke,er(nan )
me!a!(" ""k 6) ##7 akan &"per-!e*". 4ar" n"!a" p &an q.
'he #aria$les x an y are relate $y the equation y = pq x , !here p an n are constants.
4f a %raph of lo% y a%ainst x is plotte, a strai%ht line !ith %raient (, !hich passes
throu%h the point 5(,226 !oul $e o$taine. Fin the #alues of p an q.
m / Aras S
1. em'-!e* ('a* u &an # &"*('(ngkan &engan persamaan 9# % 3 6u $ 1 7# $ 5m &" mana
m "a!a* pema!ar.
'he #aria$le u an # are relate $y the equation /# = 5u + & 62 + m such that m is a
constant.
6 a 7 Apa'"!a gra0 me!a+an 6 u $ 1 7# &"p!-) sa( gar"s !(r(s me!a!(" ""k 68) ;187
&"per-!e*". 4ar" n"!a" m.
7hen the %raph # a%ainst 5 u + & 62 is plotte, a strai%ht line passin% throu%h
the point 5 *, -&* 6 is o$taine. Fin the #alue of m.
# m / Aras T
6 ' 7 Seer(sna) ,ar" ke,er(nan &an p"nasan;Y 'ag" gar"s !(r(s gra0 6 # ; u7me!a+an u#
ence, fin the %raient an Y-intercept for the strai%ht line of the %raph
5 # - u6 a%ainst u2
# m / Aras T
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 11
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MODUL 13 / TG5: HUKUM LINEAR
1=. D(a pem'-!e* ('a*) x &an y)
&"*('(ngkan &engan persamaan
&engan p &an q a&a!a* pema!ar.
B"ka gra0 me!a+an < &"!(k"s) sa( !engk(ng me!a!(" 61) =7 &"per-!e*". B"ka gra0
me!a+an &"!(k"s) sa( gar"s !(r(s &engan ke,er(nan &"per-!e*". 4ar" n"!a" p &an q.
'!o #aria$les, x an y , are
relate $y the equation !ith p
an q are constant. 4f a %raph of y #ersus x is ra!n, a cur#e passin% throu%h 5 &, 1 6 is o$taine. 4f the %raph #ersus
is ra!n, a strai%ht line !ith %raient is o$taine. Fin the #alues of p an q.
5 m / Aras T
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 12
#
px y
qx=
+
1
y
1
x
1
9
#
px y
qx=
+
1
y
1
x
1
9
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8
8
MODUL 13 / TG5: HUKUM LINEAR
1>.
Ra2a* 11/ D"agram 11
Ra2a* 11 men(n2(kkan gra0 !-g y me!a+an !-g x. D"'er" pan2ang 8 % 15 (n" &an ""k
8 a&a!a* er!eak &" aas paks";Y
Dia%ram && sho!s the %raph lo% y a%ainst lo% x. "i#en the len%th 8 = & units an
point 8 is on the Y-axis.
6a7 4ar" k--r&"na 8
Fin express y in term of x the coorinates of 8 # m / Aras S
6'7 Ungkapkan y &a!am se'(an x
Ekspress y in term of x # m / Aras S
6,7 4ar" n"!a" apa'"!a x% 19
Fin y !hen x=&/ # m / Aras S
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 13
6 1#) 11 7
!-g x
!-g y
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MODUL 13 / TG5: HUKUM LINEAR
KERTAS #
1. Ba&(a! 1 men(n2(kkan n"!a";n"!a"
'ag" pem'-!e* ('a* x &an y )
ang &"per-!e*" &ar"pa&a sa(
eksper"men. em'-!e* ('a* x &an y &"*('(ngkan -!e* persamaan ) &engan kea&aan a
&an $ "a!a* pema!ar.
'a$le 1 sho!s experimental
#alues of the #aria$les x an y!hich are relate $y the equation
, !here a an $ are constants.
x # 9 = >
y 9.# #.=# 1.> 1.33 1.1
Ba&(a! 1 / 'a$le &
6 a 7 T(karkan persamaan
kepa&a 'en(k !"nearY=$X+a, &engan kea&aan X
&an Y a&a!a* 0(ngs" &a!am x &an/aa( y.
9euce the equation to a
linear form Y=$X+a !here
X an Y are the functions of
x an3or of y.
Cerasaskan Ba&(a! 1) '"na sa( 2a&(a! 'ag" n"!a" x an& x2 y.
:ase on 'a$le &, construct a ta$le for the #alue of x an x2 y.
# m / Aras R
6 ' 7 !-kan x2 y me!a+an x &engan mengg(nakan ska!a 1 ,m kepa&a1 (n" pa&a paks"; x &an 1,m kepa&a 5 (n" pa&a paks"; x2 y. Seer(sna !(k"s sa( gar"s !(r(s
pen(a"an er'a"k .
;lot x2 y a%ainst x usin% scale of & cm to & unit on x-axis an &cm to unit on
x2 y
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MODUL 13 / TG5: HUKUM LINEAR
5 m / Aras T
#. Ba&(a! # men(n2(kkan n"!a" 'ag" &(a pem'-!e* ('a*) x &an y) &"per-!e*" &ar"pa&a sa(
eksper"men.em'-!e* ('a* < &an &"*('(ngkan -!e* persamaan y% pk x) &engan
kea&aan p &an k "a!a* pema!ar.
'a$le 2 sho!s the #alues of t!o #aria$les, x an y, o$taine from an experiment.
aria$les x an y are relate $y the equation y= pk x , !here p an k are contants.
x 1 # 3 5 9
y .9= .1# 11.8 19.53 #5.59 8.81
Ba&(a! #/ 'a$le 2
6 a 7 Terangkan 'aga"mana sa( gar"s !(r(s &apa &"!(k"s (n(k me+ak"!" persamaan
ang &"'er".
Explain ho! a strai%ht line may $e ra!n to represent the %i#en equation.
# m / Aras S
6 '7 !- !-g18 y me!a+an x &engan mengg(nakan ska!a # ,m kepa&a 1 (n" pa&a
paks"; x &an # ,m kepa&a 8.# (n" pa&a paks";!-g18 y. Seer(sna) !(k"s sa( gar"s
!(r(s pen(a"an er'a"k.
;lot lo% &* y a%ainst x $y usin% a scale of 2 cm to & unit on the x-axis an 2 cm to
*.2 unit on the lo% &* y-axis. ence, ra! the line of $est fit.
. 3 m / Aras S 6,7 G(nakan gra0 an&a &ar"pa&a 6 ' 7 (n(k men,ar" n"!a"
>se your %raph from 5$6 to fin the numerical #alue of
6 " 7 p)
6 "" 7 k .
5 m / Aras T
.
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 15
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MODUL 13 / TG5: HUKUM LINEAR
3. Ba&(a! 3 men(n2(kkan &(a pem'-!e* ('a*) x &an y ang &"per-!e*" &ar"pa&a sa(
eksper"men. em'-!e*('a* < &an &"ka"kan -!e*
persamaan
&engan kea&aan r &an n "a!a* pema!ar.
'a$le sho!s the #alues of t!o #aria$les , x an y o$taine from an experiment.
#aria$le x an y are relate $y
the equation !here r an n
are constants.
x # 3 5 9
y = 13.# #8 #.5 39.9 5.5
6a7 !- me!a+an x ) g(na ska!a # ,m kepa&a 1 (n" pa&a ke&(a;&(a paks".
Seer(sna) !(k"s gar"s !(r(s pen(a"an er'a"k.
;lot a%ainst x , usin% a scale of 2 cm to & unit on $oth axes.
ence, ra! the line of $est fit. 5 m / Aras S
6'7 G(na gra0 an&a &ar"pa&a 6a 7
>se your %raph from 5a6,
6 "7 ,ar" peng*amp"ran n"!a" 'ag" pema!ar n &an r, fin the approximate #alues of the constant n an r
6 ""7 ,ar" n"!a" apa'"!a x % 1.5
fin the #alue of y !hen x = &..
5 m / Aras T
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 16
## )n y rx xr
= +
## )n
y rx xr
= +
y
x y
x
Ba&(a! 3 / 'a$le
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MODUL 13 / TG5: HUKUM LINEAR
.
Ba&(a! / 'a$le (
Ba&(a! &"rama!kan &ar"pa&a sa( e-r" 'a*a+a &(a pem'-!e*('a*) &an )
&"*('(ngkan -!e* persamaan # % h; $ k ) &engan kea&aan h &an k a&a!a*
pema!ar.
'a$le ( is preicte from theory that t!o #aria$les, ; an , are relate $y the
equation 2 = h; + k, !here h an k are constants.
6a7 !- gra0 # me!a+an ; &engan mengg(nakan ska!a # ,m kepa&a 58 (n"
pa&a paks"; ; &an # ,m kepa&a 8.# (n" pa&a paks"; # )&an seer(sna)
!(k"s gar"s !(r(s pen(a"an er'a"k.
;lot the %raph of 2 a%ainst ; $y usin% a scale of 2 cm to * unit on the ;-axis an 2 cm to *.2 units on 2- axis ,an hence, ra! the line of $est fit.
5 m / Aras S
6'7 Dar"pa&a gra0 an&a)2a+a' s-a!an
From your %raph, ans!er the follo!in% questions
6"7 4ar" n"!a" h &an k
Fin the #alue of h an of k.
6""7 B"ka n"!a" "a!a* 1.3#) anggarkan n"!a" .
4f the #alue is &.2, estimate the #alue of ; .
5 m / Aras S
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 17
; 58 188 158 #88 #58
1.18 1.1= 1.#9 1.3 1.1
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MODUL 13 / TG5: HUKUM LINEAR
5. Ba&(a! 5 men(n2(kkan &(a pem'-!e* ('a*) x &an y) &"per-!e*" &ar"pa&a sa(
eksper"men.
'a$le sho!s the #alue of t!o #aria$les, x an y , o$taine from an experiment.
x 1.8 1.5 #.8 #.5 3.8
y 1.= #.#9 3.11 .9> . Ba&(a! 5 / 'a$le
A&a!a* &"kea*(" x &an y &"ka"kan
&engan persamaan ) &engan
kea&aan a &an $ a&a!a* pema!ar.
4t is kno!n that x an y are
relate $y the equation , !here a
an $ are constants.
6a7 Cer&asarkan 2a&(a! 5) '"na 2a&(a! 'ag" n"!a" sepa&an !-g18 y &an x2.
:ase on ta$le , construct a ta$le for the corresponin% #alues of lo% &* y
an x2.
# m / Aras R
6'7 Dengan mengg(nakan ska!a # ,m kepa&a 1 (n" kepa&a paks" x# &an # ,m
kepa&a 8.# (n"s kepa&a !-g18 y- ase your %raph to estimate the #alues of a an $.
5 m / Aras S
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 18
# xa$ y =
# xa$ y =
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MODUL 13 / TG5: HUKUM LINEAR
9. Kep((san &a!am 2a&(a! 9 &"per-!e*" se,ara eksper"men 'ag" &(a pem'-!e* ('a*) x
&an y. D"kea*(" 'a*a+a x
&"*('(ngkan &engan y -!e*
persamaan )
&engan kea&aan a &an $ "a!a* pema!ar.
'he results in the ta$le / are
o$taine experimentally for
t!o #aria$les, x an y. 4t is
kno!n that x an y are relate $y the equation , !here a an $ are constants.
x 1 # 3 5
y 1. 3.3 . 5.= 9.5
Ba&(a! 9 / 'a$le /
6a7 T(karkan persamaan ak !"near kepa&a 'en(k !"near.
)on#ert the non-linear equation into a linear form.
. # m / Aras S
6'7 L(k"s gra0 me!a+an x &engan mengg(nakan ska!a # ,m kepa&a 1 (n"
pa&a paks"; x &an # ,m kepa&a # (n" pa&a paks" .
Dra! the %raph #ersus x $y usin% a scale 2 cm to & unit on the x
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MODUL 13 / TG5: HUKUM LINEAR
&engan persamaan ) &engan kea&aan p &an k "a!a* pema!ar.
'a$le 0 sho!s that the
#aria$les, x an y are
connecte $y the equation ,
!here p an k are constants.
x # 3 5 9
y = 13.# #8 #.5 39.9 5.5
Ba&(a! / 'a$le 0
6a7 T(kar persamaan
kepa&a sa( gra0 gar"s
!(r(s ang ses(a".
)on#ert the equation
into a suita$le strai%ht line
%raph.
# m / Aras S
6'7 !- me!a+an x, g(na ska!a # ,m kepa&a 1 (n" pa&a ke&(a;&(a paks".
Seer(sna) !(k"s gar"s !(r(s pen(a"an er'a"k.
;lot a%ainst x, usin% scale of 2 cm to & unit on $oth axes. ence,
ra!
the line of $est fit.
. 3 m / Aras S
6,7 G(nakan gra0 an&a pa&a 6a7 (n(k men,ar" n"!a"
>se your %raph in 5a6 to fin the #alue of
6"7 p)
6""7 k )6"""7 y apa'"!a x = 1.#)
y !hen x = &.2,
5 m / Aras S
=. D(a k(an"") x &an y &"*('(ngkan -!e* persamaan &engan kea&aan &an
"a!a* pema!ar.
'!o quantities, x an y, are relate $y the equation !here ; an ?
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 20
xk
pkx y += ##
xk
pkx y += ##
xk
pkx y += ##
x
y
x
y
) x ;
y
?
=
) x ;
y?
=
-
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MODUL 13 / TG5: HUKUM LINEAR
are
constants.
x #.58 3=.58 3#.81 #5.58 13.88 .>=
y 1.8 1.98 #.88 #.58 3.=8 .58
6 a7 !- !-g18 y !a+an x) g(na # ,m kepa&a 5 (n" pa&a paks"; x &an # ,m
kepa&a 8.1 pa&a paks"; y. Seer(sna) !(k"s gar"s !(r(s pen(a"an er'a"k.
;lot lo% &* y a%ainst x, $y usin% a scale of 2 cm to units on the x-axis an 2 cm
to *.& units on the y-axis. ence, ra! th line of $est fit.
m / Aras S
6 '7 G(na gra0 &ar"pa&a 6a7 (n(k ,ar" n"!a"
>se the %raph from 5a6 to fin the #alue of
6"7 ;
6""7 ?
6"""7 y apa'"!a x % 15.5
y !hen x = &.
9 m / Aras S
>.
x #.8 3.8 .8 5.8 9.8
y 5.5= 9.5> .3 =.1= =.=9
6a7 L(k"s gra0 !-g y me!a+an !-g x
Dra! the %raph of lo% y #ersus lo% x
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 21
-
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MODUL 13 / TG5: HUKUM LINEAR
5 m / Aras S
6'7 T(!"s *('(ngan anara x &an y &a!am persamaan 'er'en(k
7rite o!n the relationship associatin% x an y as an equation in the form
6 "7 !-gar"ma
lo%arithm
6""7 "n&eks 4nex
3 m / Aras T
6,7 K"ra n"!a" x apa'"!a y % >
)alculate the #alue of x !hen y =
# m / Aras T
18. D(a -rang pe!a2ar men2a!ankan sa( eksper"men (n(k mengka2" sesaran ses(a( -'2ek)
c ,m &ar" sa( ""k pa&a t saa. Sa!a* sa( &ar"pa&a mereka memer*a" masa &an se-rang
!ag" men,aa sesaran.Kep((san &"(n2(kkan &a!am Ba&(a! =.
'!o stuents conucte an experiment to stuy the isplacement of an o$@ect, c cm from a point at t secon. ne of them o$ser#e the time the other one recore the
isplacemen . 'he results are sho!n in ta$le 1.
T"me) t
6se,-n&7#8 8 98 188 1#8 198
D"sp!a,emen)
s 6meer79.= 19. 3>.5 9= >8 1=.=
Ba&(a! = / 'a$le 1
Sa!a* sa( n"!a" 'ag" s &"sak" "&ak epa.
ne of the #alue of s is $elie#e to $e inaccurate. 6a7 Dra+ *e grap* ers(s t
Aukis %raf mela!an t m / Aras S
6'7 6 "7 Mana sa( n"!a" s a&a!a* "&ak epa &an ,ar" n"!a" ang sepa(na.
7hich #alue of s is inaccurate an fin its correct #alue.
# m / Aras T
6""7 Cerasaskan gra0 an&a) ,ar" n"!a";n"!a" a &an ( 2"ka s &an &"ka"kan &engan
persamaan s = ut +at 2 &engan kea&aan a &an u "a!a* pema!ar.
:ase on your %raph, fin the #alues of a an u if s an t is relate $y the
equation s = ut +at 2
such that a an u are constant.. m / Aras T
11.
T"me) t
6se,-n&71 # 3 5 9
D"sp!a,emen)
s 6meer73.5 =.9 15.> #.8 39.8 k 91.5
Ba&(a! > / 'a$le
Ba&(a! > men(n2(kkan n"!a" 'ag" sesaran) s meer &an masa ) t saa ses(a( -'2ek
'ergerak. D"'er" s = ut +at 2) &engan u "a!a* *a!a2( a+a! &an a "a!a* pe,(an -'2ek.
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 22
s
t s
t
1
#
-
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MODUL 13 / TG5: HUKUM LINEAR
'a$le sho!s the #alues of isplacement, s meter an time, t secons of a mo#in% o$@ect.
"i#en s = ut +at 2 , such that u is the initial #elocity an a is the acceleration of the
o$@ect.
6 a 7 L(k"s gra0 me!a+an t .
Dra! the %raph #ersus t.
m / Aras T 6' 7 Cer&asarkan gra0 an&a) ,ar"
:ase on your %raph, fin
6"7 *a!a2( a+a!
initial #elocity
6""7 e,(an
acceleration,
6""7 n"!a" k
the #alue of k
9 m / Aras T
1#. Ba&(a! > men(n2(kkan n"!a" 'ag" pem'-!e* ('a* u &an #) &"per-!e*" &ar" sa(
eksper"men. 'a$le sho!s #alues of #aria$les u an #, !hich are o$taine from an experiment .
u 1# 15 #8 #= 8
# >.3 11.5 1 1 ##
Ba&(a! > / 'a$le
6a7 A&a!a* &"kea*(" 'a*a+a (
&an &"*('(ngkan -!e*
persamaan ) &engan kea&aan k
"a!a* pema!ar. Terangkan 'aga"mana sa( gra0 gar"s !(r(s &apa &"!(k"s (n(k
me+ak"!" persamaan "n".
MODUL SOLAF MATEMATIK TAMBAHAN M13 - 23
1
#
s
t s
t
1 1k
# u= +
-
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MODUL 13 / TG5: HUKUM LINEAR
4t is kno!n that u an # are
connecte $y the equation ,
!here k is a constant.
Explain ho! a strai%ht line %raph can $e ra!n to represent this equation.
5 m / Aras T
6'7 Seer(sna) &engan mengg(nakan ska!a #,m kepa&a 8.81 (n" pa&a ke&(a;&(a
paks") !(k"s gra0 me!a+an (n(k peng*amp"ran n"!a" 'ag" k.
ence, $y usin% a scale of 2cm to *.*& unit on $oth axes, ra! the %raph of
a%ainst to etermine the approximate #alue of k
5 m / Aras T
MODUL SOLAF MATEMATIK TAMBAHAN M13 24
1 1k
# u= +
1
#
1
u1
#1
u
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