© Glencoe/McGraw-Hill A2 Glencoe Algebra 2
Answers (Lesson 1-1)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Exp
ress
ion
s an
d F
orm
ula
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill1
Gle
ncoe
Alg
ebra
2
Lesson 1-1
Ord
er o
f O
per
atio
ns
1.S
impl
ify t
he e
xpre
ssio
ns in
side
gro
upin
g sy
mbo
ls.
Ord
er o
f2.
Eva
luat
e al
l pow
ers.
Op
erat
ion
s3.
Do
all m
ultip
licat
ions
and
div
isio
ns f
rom
left
to r
ight
.4.
Do
all a
dditi
ons
and
subt
ract
ions
fro
m le
ft to
rig
ht.
Eva
luat
e [1
8 �
(6 �
4)]
�2.
[18
�(6
�4)
] �
2 �
[18
�10
] �
2�
8 �
2�
4
Eva
luat
e 3x
2�
x(y
�5)
if x
�3
and
y�
0.5.
Rep
lace
eac
h va
riab
le w
ith
the
give
n va
lue.
3x2
�x(
y�
5) �
3 �
(3)2
�3(
0.5
�5)
�3
�(9
) �
3(�
4.5)
�27
�13
.5�
13.5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.14
�(6
�2)
172.
11 �
(3 �
2)2
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64
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55.
(5 �
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144
6.52
��
18 �
234
.25
7.�
68.
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20 �
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611
10.1
2 �
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611
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12.6
(7)
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38
13.8
(42
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240
14.
�24
15.
4
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�8.
2,b
��
3,c
�4,
and
d�
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16.
49.2
17.5
(6c
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d)
215
18.
�6
19.a
c�
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.(b
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25.a
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7.45
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8.7
a� b
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a � dc2�
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ab � d
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9 �
3 �
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16 �
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1 � 4
©G
lenc
oe/M
cGra
w-H
ill2
Gle
ncoe
Alg
ebra
2
Form
ula
sA
for
mu
lais
a m
ath
emat
ical
sen
ten
ce t
hat
use
s va
riab
les
to e
xpre
ss t
he
rela
tion
ship
bet
wee
n c
erta
in q
uan
titi
es.I
f yo
u k
now
th
e va
lue
of e
very
var
iabl
e ex
cept
on
ein
a f
orm
ula
,you
can
use
su
bsti
tuti
on a
nd
the
orde
r of
ope
rati
ons
to f
ind
the
valu
e of
th
eu
nkn
own
var
iabl
e. To
calc
ula
te t
he
nu
mb
er o
f re
ams
of p
aper
nee
ded
to
pri
nt
nco
pie
s
of a
boo
kle
t th
at i
s p
pag
es l
ong,
you
can
use
th
e fo
rmu
la r
�,w
her
e r
is t
he
nu
mb
er o
f re
ams
nee
ded
.How
man
y re
ams
of p
aper
mu
st y
ou b
uy
to p
rin
t 17
2 co
pie
s of
a 2
5-p
age
boo
kle
t?
Su
bsti
tute
n�
172
and
p�
25 i
nto
th
e fo
rmu
la r
�.
r� � �
8.6
You
can
not
bu
y 8.
6 re
ams
of p
aper
.You
wil
l n
eed
to b
uy
9 re
ams
to p
rin
t 17
2 co
pies
.
For
Exe
rcis
es 1
–3,u
se t
he
foll
owin
g in
form
atio
n.
For
a s
cien
ce e
xper
imen
t,S
arah
cou
nts
th
e n
um
ber
of b
reat
hs
nee
ded
for
her
to
blow
up
abe
ach
bal
l.S
he
wil
l th
en f
ind
the
volu
me
of t
he
beac
h b
all
in c
ubi
c ce
nti
met
ers
and
divi
deby
th
e n
um
ber
of b
reat
hs
to f
ind
the
aver
age
volu
me
of a
ir p
er b
reat
h.
1.H
er b
each
bal
l h
as a
rad
ius
of 9
in
ches
.Fir
st s
he
con
vert
s th
e ra
diu
s to
cen
tim
eter
su
sin
g th
e fo
rmu
la C
�2.
54I,
wh
ere
Cis
a l
engt
h i
n c
enti
met
ers
and
Iis
th
e sa
me
len
gth
in i
nch
es.H
ow m
any
cen
tim
eter
s ar
e th
ere
in 9
in
ches
?22
.86
cm
2.T
he
volu
me
of a
sph
ere
is g
iven
by
the
form
ula
V�
�r3
,wh
ere
Vis
th
e vo
lum
e of
th
e
sph
ere
and
ris
its
rad
ius.
Wh
at i
s th
e vo
lum
e of
th
e be
ach
bal
l in
cu
bic
cen
tim
eter
s?(U
se 3
.14
for
�.)
50,0
15 c
m3
3.S
arah
tak
es 4
0 br
eath
s to
blo
w u
p th
e be
ach
bal
l.W
hat
is
the
aver
age
volu
me
of a
ir p
erbr
eath
?ab
ou
t 12
50 c
m3
4.A
per
son
’s b
asal
met
abol
ic r
ate
(or
BM
R)
is t
he
nu
mbe
r of
cal
orie
s n
eede
d to
su
ppor
t h
isor
her
bod
ily
fun
ctio
ns
for
one
day.
Th
e B
MR
of
an 8
0-ye
ar-o
ld m
an i
s gi
ven
by
the
form
ula
BM
R �
12w
�(0
.02)
(6)1
2w,w
her
e w
is t
he
man
’s w
eigh
t in
pou
nds
.Wh
at i
s th
eB
MR
of
an 8
0-ye
ar-o
ld m
an w
ho
wei
ghs
170
pou
nds
?17
95 c
alo
ries
4 � 3
43,0
00�
500
(172
)(25
)�
�50
0
np
� 500
np
� 500
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Exp
ress
ion
s an
d F
orm
ula
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-1)
Skil
ls P
ract
ice
Exp
ress
ion
s an
d F
orm
ula
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill3
Gle
ncoe
Alg
ebra
2
Lesson 1-1
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.18
�2
�3
272.
9 �
6 �
2 �
113
3.(3
�8)
2 (4)
�3
974.
5 �
3(2
�12
�2)
�7
5.�
[�9
�10
(3)]
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68 �
7)32
�43
152
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(5)
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8 �
22]5
�85
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e ea
ch e
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ssio
n i
f r
��
1,s
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t�
12,v
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and
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9.6r
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010
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s84
11.w
(s�
r)�
212
.s�
2r�
16v
1
13.(
4s)2
144
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2 r�
wt
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15.2
(3r
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) �
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r2�
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t10
520
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21.T
EMPE
RA
TUR
ET
he
form
ula
K�
C�
273
give
s th
e te
mpe
ratu
re i
n k
elvi
ns
(K)
for
agi
ven
tem
pera
ture
in
deg
rees
Cel
siu
s.W
hat
is
the
tem
pera
ture
in
kel
vin
s w
hen
th
ete
mpe
ratu
re i
s 55
deg
rees
Cel
siu
s?32
8 K
22.T
EMPE
RA
TUR
ET
he
form
ula
C�
(F�
32)
give
s th
e te
mpe
ratu
re i
n d
egre
es C
elsi
us
for
a gi
ven
tem
pera
ture
in
deg
rees
Fah
ren
hei
t.W
hat
is
the
tem
pera
ture
in
deg
rees
Cel
siu
s w
hen
th
e te
mpe
ratu
re i
s 68
deg
rees
Fah
ren
hei
t?20
�C
5 � 9
2w �r
rv3
� s225 � 2
3v�
t� 5s
�t
1 � 2
6(7
�5)
�� 4
1 � 3
©G
lenc
oe/M
cGra
w-H
ill4
Gle
ncoe
Alg
ebra
2
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.3(
4 �
7) �
11�
202.
4(12
�42
)�
16
3.1
�2
�3(
4) �
2�
34.
12 �
[20
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62�
3 �
22)]
88
5.20
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(3)
856.
(�2)
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(3)(
8) �
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10)
18
7.18
�{5
�[3
4 �
(17
�11
)]}
418.
[4(5
�3)
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4 �
8)]
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1
9.[6
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510
.[�
5 �
5(�
3)]
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11.
3212
.�
(�1)
2�
4(�
9)�
53
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�,b
��
8,c
��
2,d
�3,
and
e�
.
13.a
b2�
d45
14.(
c�
d)b
�8
15.
�d
212
16.
12
17.(
b�
de)
e2�
118
.ac3
�b2
de
�70
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b[a
�(c
�d
)2]
206
20.
�22
21.9
bc�
141
22.2
ab2
�(d
3�
c)67
23.T
EMPE
RA
TUR
ET
he
form
ula
F�
C�
32 g
ives
th
e te
mpe
ratu
re i
n d
egre
es
Fah
ren
hei
t fo
r a
give
n t
empe
ratu
re i
n d
egre
es C
elsi
us.
Wh
at i
s th
e te
mpe
ratu
re i
nde
gree
s Fa
hre
nh
eit
wh
en t
he
tem
pera
ture
is
�40
deg
rees
Cel
siu
s?�
40�F
24.P
HY
SIC
ST
he
form
ula
h�
120t
�16
t2gi
ves
the
hei
ght
hin
fee
t of
an
obj
ect
tse
con
dsaf
ter
it i
s sh
ot u
pwar
d fr
om E
arth
’s s
urf
ace
wit
h a
n i
nit
ial
velo
city
of
120
feet
per
seco
nd.
Wh
at w
ill
the
hei
ght
of t
he
obje
ct b
e af
ter
6 se
con
ds?
144
ft
25.A
GR
ICU
LTU
RE
Fait
h o
wn
s an
org
anic
app
le o
rch
ard.
Fro
m h
er e
xper
ien
ce t
he
last
few
seas
ons,
she
has
dev
elop
ed t
he
form
ula
P�
20x
�0.
01x2
�24
0 to
pre
dict
her
pro
fit
Pin
doll
ars
this
sea
son
if
her
tre
es p
rodu
ce x
bush
els
of a
pple
s.W
hat
is
Fait
h’s
pre
dict
edpr
ofit
th
is s
easo
n i
f h
er o
rch
ard
prod
uce
s 30
0 bu
shel
s of
app
les?
$486
0
9 � 5
1 � e
c � e2ac
4�dd(b
� c
)�
acab � c
1 � 33 � 4
(�8)
2� 5
�9
�8(
13 �
37)
�� 6
1 � 41 � 2
Pra
ctic
e (
Ave
rag
e)
Exp
ress
ion
s an
d F
orm
ula
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
© Glencoe/McGraw-Hill A8 Glencoe Algebra 2
Answers (Lesson 1-3)
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill13
Gle
ncoe
Alg
ebra
2
Lesson 1-3
Ver
bal
Exp
ress
ion
s to
Alg
ebra
ic E
xpre
ssio
ns
Th
e ch
art
sugg
ests
som
e w
ays
toh
elp
you
tra
nsl
ate
wor
d ex
pres
sion
s in
to a
lgeb
raic
exp
ress
ion
s.A
ny
lett
er c
an b
e u
sed
tore
pres
ent
a n
um
ber
that
is
not
kn
own
.
Wo
rd E
xpre
ssio
nO
per
atio
n
and,
plu
s, s
um,
incr
ease
d by
, m
ore
than
addi
tion
min
us,
diffe
renc
e, d
ecre
ased
by,
less
tha
nsu
btra
ctio
n
times
, pr
oduc
t, of
(as
in
of a
num
ber)
mul
tiplic
atio
n
divi
ded
by,
quot
ient
divi
sion
1 � 2
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
18 l
ess
than
the
qu
otie
nt
of a
nu
mb
er a
nd
3.
�18
n � 3
Wri
te a
ver
bal
sen
ten
ce t
ore
pre
sen
t 6(
n�
2) �
14.
Six
tim
es t
he
diff
eren
ce o
f a
nu
mbe
r an
d tw
ois
equ
al t
o 14
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.th
e su
m o
f si
x ti
mes
a n
um
ber
and
256n
�25
2.fo
ur
tim
es t
he
sum
of
a n
um
ber
and
34(
n�
3)
3.7
less
th
an f
ifte
en t
imes
a n
um
ber
15n
� 7
4.th
e di
ffer
ence
of
nin
e ti
mes
a n
um
ber
and
the
quot
ien
t of
6 a
nd
the
sam
e n
um
ber9n
�
5.th
e su
m o
f 10
0 an
d fo
ur
tim
es a
nu
mbe
r10
0 �
4n
6.th
e pr
odu
ct o
f 3
and
the
sum
of
11 a
nd
a n
um
ber
3(11
�n
)
7.fo
ur
tim
es t
he
squ
are
of a
nu
mbe
r in
crea
sed
by f
ive
tim
es t
he
sam
e n
um
ber
4n2
�5n
8.23
mor
e th
an t
he
prod
uct
of
7 an
d a
nu
mbe
r7n
�23
Wri
te a
ver
bal
sen
ten
ce t
o re
pre
sen
t ea
ch e
qu
atio
n.
Sam
ple
an
swer
s ar
e g
iven
.
9.3n
�35
�79
Th
e d
iffe
ren
ce o
f th
ree
tim
es a
nu
mb
er a
nd
35
is e
qu
al t
o 7
9.
10.2
(n3
�3n
2 ) �
4nTw
ice
the
sum
of
the
cub
e o
f a
nu
mb
er a
nd
th
ree
tim
es t
he
squ
are
of
the
nu
mb
er is
eq
ual
to
fo
ur
tim
es t
he
nu
mb
er.
11.�
n5 �n
3�
�n
�8
Th
e q
uo
tien
t o
f fi
ve t
imes
a n
um
ber
an
d t
he
sum
of
the
nu
mb
eran
d 3
is e
qu
al t
o t
he
dif
fere
nce
of
the
nu
mb
er a
nd
8.6 � n
©G
lenc
oe/M
cGra
w-H
ill14
Gle
ncoe
Alg
ebra
2
Pro
per
ties
of
Equ
alit
yYo
u c
an s
olve
equ
atio
ns
by u
sin
g ad
diti
on,s
ubt
ract
ion
,m
ult
ipli
cati
on,o
r di
visi
on.
Ad
dit
ion
an
d S
ub
trac
tio
nF
or a
ny r
eal n
umbe
rs a
, b,
and
c,
if a
�b,
Pro
per
ties
of
Eq
ual
ity
then
a�
c�
b�
can
d a
�c
�b
�c.
Mu
ltip
licat
ion
an
d D
ivis
ion
For
any
rea
l num
bers
a,
b, a
nd c
,if
a�
b,
Pro
per
ties
of
Eq
ual
ity
then
a�
c�
b�
can
d, if
cis
not
zer
o,
�.
b � ca � c
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
Sol
ve 1
00 �
8x�
140.
100
�8x
�14
010
0 �
8x�
100
�14
0 �
100
�8x
�40
x�
�5
Sol
ve 4
x�
5y�
100
for
y.
4x�
5y�
100
4x�
5y�
4x�
100
�4x
5y�
100
�4x
y�
(100
�4x
)
y�
20 �
x4 � 5
1 � 5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
1.3s
�45
152.
17 �
9 �
a�
83.
5t�
1 �
6t�
54
4.m
�5.
7 �
x�
38
6.�
8 �
�2(
z�
7)�
3
7.0.
2b�
1050
8.3x
�17
�5x
�13
159.
5(4
�k)
��
10k
�4
10.1
20 �
y�
6080
11.
n�
98 �
n28
12.4
.5 �
2p�
8.7
2.1
13.4
n�
20 �
53 �
2n5
14.1
00 �
20 �
5r�
1615
.2x
�75
�10
2 �
x9
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
16.a
�3b
�c,
for
bb
�17
.�
10,f
or t
t�
18.h
�12
g�
1,fo
r g
g�
19.
�12
,for
pp
�
20.2
xy�
x�
7,fo
r x
x�
21.
��
6,fo
r f
f�
24 �
2d
22.3
(2j
�k)
�10
8,fo
r j
j�18
�23
.3.5
s�
42 �
14t,
for
ss
�4t
�12
24.
�5m
�20
,for
mm
�25
.4x
�3y
�10
,for
yy
�x
�10 � 3
4 � 320
n� 5n
�1
m � n
k � 2
f � 4d � 2
7� 2y
�1
4r � q3p
q�
rh
�1
�12
s � 20s � 2t
a�
c�
3
1 � 2
5 � 23 � 4
1 � 23 � 4
1 � 22 � 3
© Glencoe/McGraw-Hill A9 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-3)
Skil
ls P
ract
ice
So
lvin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill15
Gle
ncoe
Alg
ebra
2
Lesson 1-3
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.4
tim
es a
nu
mbe
r,in
crea
sed
by 7
2.8
less
th
an 5
tim
es a
nu
mbe
r
4n�
75n
�8
3.6
tim
es t
he
sum
of
a n
um
ber
and
54.
the
prod
uct
of 3
and
a n
umbe
r,di
vide
d by
9
6(n
�5)
5.3
tim
es t
he
diff
eren
ce o
f 4
and
a n
um
ber
3(4
�n
)
6.th
e pr
odu
ct o
f �
11 a
nd
the
squ
are
of a
nu
mbe
r�
11n
2
Wri
te a
ver
bal
exp
ress
ion
to
rep
rese
nt
each
eq
uat
ion
.7–
10.S
amp
le a
nsw
ers
7.n
�8
�16
8.8
�3x
�5
are
giv
en.
Th
e d
iffe
ren
ce o
f a
nu
mb
er
Th
e su
m o
f 8
and
3 t
imes
a
and
8 is
16.
nu
mb
er is
5.
9.b2
�3
�b
10.
�2
�2y
Th
ree
add
ed t
o t
he
squ
are
of
A n
um
ber
div
ided
by
3 is
th
ea
nu
mb
er is
th
e n
um
ber
.d
iffe
ren
ce o
f 2
and
tw
ice
the
nu
mb
er.
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch s
tate
men
t.
11.I
f a
�0.
5b,a
nd
0.5b
�10
,th
en a
�10
.12
.If
d�
1 �
f,th
en d
�f
�1.
Tran
siti
ve (
�)
Su
btr
acti
on
(�
)
13.I
f �
7x�
14,t
hen
14
��
7x.
14.I
f (8
�7)
r�
30,t
hen
15r
�30
.S
ymm
etri
c (�
)S
ub
stit
uti
on
(�
)
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
15.4
m�
2 �
184
16.x
�4
�5x
�2
17.3
t�
2t�
55
18.�
3b�
7 �
�15
�2b
19.�
5x�
3x�
243
20.4
v�
20 �
6 �
345
21.a
��
35
22.2
.2n
�0.
8n�
5 �
4n5
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
23.I
�pr
t,fo
r p
p�
24.y
�x
�12
,for
xx
�4y
�48
25.A
�,f
or y
y�
2A�
x26
.A�
2�r2
�2�
rh,f
or h
h�
A�
2r2
��
2r
x�
y�
2
1 � 4I � rt
2a � 5
22 � 5
1 � 2
y � 33n � 9
©G
lenc
oe/M
cGra
w-H
ill16
Gle
ncoe
Alg
ebra
2
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.2
mor
e th
an t
he q
uoti
ent
of a
num
ber
and
52.
the
sum
of
two
con
secu
tive
in
tege
rs
�2
n�
(n�
1)
3.5
tim
es t
he
sum
of
a n
um
ber
and
14.
1 le
ss t
han
tw
ice
the
squ
are
of a
nu
mbe
r5(
m�
1)2y
2�
1
Wri
te a
ver
bal
exp
ress
ion
to
rep
rese
nt
each
eq
uat
ion
.5–
8.S
amp
le a
nsw
ers
5.5
�2x
�4
6.3y
�4y
3ar
e g
iven
.
Th
e d
iffe
ren
ce o
f 5
and
tw
ice
a T
hre
e ti
mes
a n
um
ber
is 4
tim
es
nu
mb
er is
4.
the
cub
e o
f th
e n
um
ber
.
7.3c
�2(
c�
1)8.
�3(
2m�
1)T
he
qu
oti
ent
Th
ree
tim
es a
nu
mb
er is
tw
ice
the
of
a n
um
ber
an
d 5
is 3
tim
es t
he
dif
fere
nce
of
the
nu
mb
er a
nd
1.
sum
of
twic
e th
e n
um
ber
an
d 1
.
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch s
tate
men
t.
9.If
t�
13 �
52,t
hen
52
�t
�13
.10
.If
8(2q
�1)
�4,
then
2(2
q�
1) �
1.S
ymm
etri
c (�
)D
ivis
ion
(�
)
11.I
f h
�12
�22
,th
en h
�10
.12
.If
4m�
�15
,th
en �
12m
�45
.S
ub
trac
tio
n (
�)
Mu
ltip
licat
ion
(�
)
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
13.1
4 �
8 �
6r�
114
.9 �
4n�
�59
�17
15.
�n
�16
.s
��
17.�
1.6r
�5
��
7.8
818
.6x
�5
�7
�9x
19.5
(6 �
4v)
�v
�21
20.6
y�
5 �
�3(
2y�
1)
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
21.E
�m
c2,f
or m
m�
22.c
�,f
or d
d�
23.h
�vt
�gt
2 ,fo
r v
v�
24.E
�Iw
2�
U,f
or I
I�
Def
ine
a va
riab
le,w
rite
an
eq
uat
ion
,an
d s
olve
th
e p
rob
lem
.
25.G
EOM
ETRY
Th
e le
ngt
h o
f a
rect
angl
e is
tw
ice
the
wid
th.F
ind
the
wid
th i
f th
epe
rim
eter
is
60 c
enti
met
ers.
w�
wid
th;
2(2w
) �
2w�
60;
10 c
m
26.G
OLF
Lui
s an
d th
ree
frie
nds
wen
t go
lfin
g.T
wo
of t
he f
rien
ds r
ente
d cl
ubs
for
$6 e
ach.
The
tota
l cos
t of
the
ren
ted
club
s an
d th
e gr
een
fees
for
eac
h pe
rson
was
$76
.Wha
t w
as t
he c
ost
of t
he g
reen
fee
s fo
r ea
ch p
erso
n?g
�g
reen
fee
s p
er p
erso
n;6
(2)
�4g
�76
;$16
2(E
�U
)�
�w
21 � 2
h�
gt2
�t
3c�
1�
22d
�1
�3
E � c2
1 � 63 � 7
4 � 5
1 � 511 � 12
3 � 45 � 6
1 � 45 � 8
1 � 23 � 4
m � 5
y � 5
Pra
ctic
e (
Ave
rag
e)
So
lvin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
© Glencoe/McGraw-Hill A14 Glencoe Algebra 2
Answers (Lesson 1-5)
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill25
Gle
ncoe
Alg
ebra
2
Lesson 1-5
Solv
e In
equ
alit
ies
Th
e fo
llow
ing
prop
erti
es c
an b
e u
sed
to s
olve
in
equ
alit
ies.
Ad
dit
ion
an
d S
ub
trac
tio
n P
rop
erti
es f
or
Ineq
ual
itie
sM
ult
iplic
atio
n a
nd
Div
isio
n P
rop
erti
es f
or
Ineq
ual
itie
s
For
any
rea
l num
bers
a,
b, a
nd c
:F
or a
ny r
eal n
umbe
rs a
, b,
and
c,
with
c�
0:1.
If a
�b,
the
n a
�c
�b
�c
and
a�
c�
b�
c.1.
If c
is p
ositi
ve a
nd a
�b,
the
n ac
�bc
and
�.
2.If
a
b, t
hen
a�
c
b�
can
d a
�c
b
�c.
2.If
cis
pos
itive
and
a
b, t
hen
ac
bcan
d
.
3.If
cis
neg
ativ
e an
d a
�b,
the
n ac
bc
and
.
4.If
cis
neg
ativ
e an
d a
b,
the
n ac
�bc
and
�.
Th
ese
prop
erti
es a
re a
lso
tru
e fo
r �
and
�.
b � ca � c
b � ca � c
b � ca � c
b � ca � c
Sol
ve 2
x�
4
36.
Th
en g
rap
h t
he
solu
tion
set
on
an
um
ber
lin
e.
2x�
4 �
4
36 �
42x
32
x
16T
he
solu
tion
set
is
{xx
16
}.
2120
1918
1716
1514
13
Sol
ve 1
7 �
3w�
35.T
hen
grap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
17 �
3w�
3517
�3w
�17
�35
�17
�3w
�18
w�
�6
Th
e so
luti
on s
et i
s (�
�,�
6].
�9
�8
�7
�6
�5
�4
�3
�2
�1
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er o
r in
terv
aln
otat
ion
.Th
en g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.7(
7a�
9) �
842.
3(9z
�4)
35
z�
43.
5(12
�3n
) �
165
{aa
�3}
or
(�∞
,3]
{zz
�2}
or
(�∞
,2)
{nn
�
7} o
r (�
7,�
∞)
4.18
�4k
�2(
k�
21)
5.4(
b�
7) �
6 �
226.
2 �
3(m
�5)
�4(
m�
3)
{kk
�
4} o
r (�
4,�
∞)
{bb
�11
} o
r (�
∞,1
1){m
m�
5} o
r (�
∞,5
]
7.4x
�2
�
7(4x
�2)
8.(2
y�
3)
y�
29.
2.5d
�15
�75
�xx
�o
r �
,�∞�
{yy
��
9} o
r (�
∞,�
9){d
d�
24}
or
(�∞
,24]
2122
1920
2324
2526
27�
12�
14�
10�
8�
6�
4�
3�
2�
10
12
34
1 � 21 � 2
1 � 3
23
01
45
67
88
96
710
1112
1314
�8
�7
�6
�5
�4
�3
�2
�1
0
�8
�7
�6
�5
�4
�3
�2
�1
0�
2�
1�
4�
30
12
34
�2
�1
�4
�3
01
23
4
©G
lenc
oe/M
cGra
w-H
ill26
Gle
ncoe
Alg
ebra
2
Rea
l-W
orl
d P
rob
lem
s w
ith
Ineq
ual
itie
sM
any
real
-wor
ld p
robl
ems
invo
lve
ineq
ual
itie
s.T
he
char
t be
low
sh
ows
som
e co
mm
on p
hra
ses
that
in
dica
te i
neq
ual
itie
s.
�
��
is le
ss t
han
is g
reat
er t
han
is a
t m
ost
is a
t le
ast
is f
ewer
tha
nis
mor
e th
anis
no
mor
e th
anis
no
less
tha
nis
less
tha
n or
equ
al t
ois
gre
ater
tha
n or
equ
al t
o
SPO
RTS
Th
e V
ikin
gs p
lay
36 g
ames
th
is y
ear.
At
mid
seas
on,t
hey
hav
e w
on 1
6 ga
mes
.How
man
y of
th
e re
mai
nin
g ga
mes
mu
st t
hey
win
in
ord
er t
ow
in a
t le
ast
80%
of
all
thei
r ga
mes
th
is s
easo
n?
Let
xbe
th
e n
um
ber
of r
emai
nin
g ga
mes
th
at t
he
Vik
ings
mu
st w
in.T
he
tota
l n
um
ber
ofga
mes
th
ey w
ill
hav
e w
on b
y th
e en
d of
th
e se
ason
is
16 �
x.T
hey
wan
t to
win
at
leas
t 80
%of
th
eir
gam
es.W
rite
an
in
equ
alit
y w
ith
�.
16 �
x�
0.8(
36)
x�
0.8(
36)
�16
x�
12.8
Sin
ce t
hey
can
not
win
a f
ract
ion
al p
art
of a
gam
e,th
e V
ikin
gs m
ust
win
at
leas
t 13
of
the
gam
es r
emai
nin
g.
1.PA
RK
ING
FEE
ST
he
city
par
kin
g lo
t ch
arge
s $2
.50
for
the
firs
t h
our
and
$0.2
5 fo
r ea
chad
diti
onal
hou
r.If
th
e m
ost
you
wan
t to
pay
for
par
kin
g is
$6.
50,s
olve
th
e in
equ
alit
y2.
50 �
0.25
(x�
1) �
6.50
to
dete
rmin
e fo
r h
ow m
any
hou
rs y
ou c
an p
ark
you
r ca
r.A
t m
ost
17
ho
urs
PLA
NN
ING
For
Exe
rcis
es 2
an
d 3
,use
th
e fo
llow
ing
info
rmat
ion
.
Eth
an i
s re
adin
g a
482-
page
boo
k fo
r a
book
rep
ort
due
on M
onda
y.H
e h
as a
lrea
dy r
ead
80 p
ages
.He
wan
ts t
o fi
gure
ou
t h
ow m
any
page
s pe
r h
our
he
nee
ds t
o re
ad i
n o
rder
to
fin
ish
th
e bo
ok i
n l
ess
than
6 h
ours
.
2.W
rite
an
in
equ
alit
y to
des
crib
e th
is s
itu
atio
n.
�6
or
6n�
482
�80
3.S
olve
the
ine
qual
ity
and
inte
rpre
t th
e so
luti
on.
Eth
an m
ust
rea
d a
t le
ast
67 p
ages
per
ho
ur
in o
rder
to
fin
ish
th
e b
oo
k in
less
th
an 6
ho
urs
.
BO
WLI
NG
For
Exe
rcis
es 4
an
d 5
,use
th
e fo
llow
ing
info
rmat
ion
.
Fou
r fr
ien
ds p
lan
to
spen
d F
rida
y ev
enin
g at
th
e bo
wli
ng
alle
y.T
hre
e of
th
e fr
ien
ds n
eed
tore
nt
shoe
s fo
r $3
.50
per
pers
on.A
str
ing
(gam
e) o
f bo
wli
ng
cost
s $1
.50
per
pers
on.I
f th
efr
ien
ds p
ool
thei
r $4
0,h
ow m
any
stri
ngs
can
th
ey a
ffor
d to
bow
l?
4.W
rite
an
equ
atio
n t
o de
scri
be t
his
sit
uat
ion
.3(
3.50
) �
4(1.
50)n
�40
5.S
olve
th
e in
equ
alit
y an
d in
terp
ret
the
solu
tion
.T
he
frie
nd
s ca
n b
ow
l at
mo
st
4 st
rin
gs.
482
�80
�� n
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-5)
Skil
ls P
ract
ice
So
lvin
g In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill27
Gle
ncoe
Alg
ebra
2
Lesson 1-5
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er o
r in
terv
aln
otat
ion
.Th
en,g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.�
2{z
z�
�8}
or
(�∞
,�8]
2.3a
�7
�16
{aa
�3}
or
(�∞
,3]
3.16
�3q
�4
{qq
4}
or
(4,∞
)4.
20 �
3s
7s{s
s�
2} o
r (�
∞,2
)
5.3x
��
9{x
x�
�3}
or
[�3,
∞)
6.4b
�9
�7
{bb
�4}
or
(�∞
,4]
7.2z
��
9 �
5z{z
z
3} o
r (3
,∞)
8.7f
�9
3f
�1
{ff
2}
or
(2,∞
)
9.�
3s�
8 �
5s{s
s�
�1}
or
[�1,
∞)
10.7
t�
(t�
4) �
25�t
t�
�or ��
∞,
�
11.0
.7m
�0.
3m�
2m�
4{m
m�
4}12
.4(5
x�
7) �
13�x
x�
��o
ro
r (�
∞,4
]��
∞,�
�13
.1.7
y�
0.78
5
{yy
3.
4}14
.4x
�9
2x
�1
{xx
5}
or
(5,∞
)o
r (3
.4,∞
)
Def
ine
a va
riab
le a
nd
wri
te a
n i
neq
ual
ity
for
each
pro
ble
m.T
hen
sol
ve.
15.N
inet
een
mor
e th
an a
nu
mbe
r is
les
s th
an 4
2.n
�19
�42
;n
�23
16.T
he
diff
eren
ce o
f th
ree
tim
es a
nu
mbe
r an
d 16
is
at l
east
8.
3n�
16 �
8;n
�8
17.O
ne h
alf
of a
num
ber
is m
ore
than
6 l
ess
than
the
sam
e nu
mbe
r.n
n
�6;
n�
12
18.F
ive
less
th
an t
he
prod
uct
of
6 an
d a
nu
mbe
r is
no
mor
e th
an t
wic
e th
at s
ame
nu
mbe
r.
6n�
5 �
2n;
n�
5 � 4
1 � 2
�1
01
23
45
67
�1
�2
01
23
45
6
3 � 4�
2�
1�
4�
30
12
34
�2
�1
01
23
45
6
3 � 4
�2
�1
�4
�3
01
23
4�
1�
2�
3�
40
12
34
7 � 27 � 2
�1
�2
�3
�4
01
23
4�
1�
20
12
34
56
�2
�1
01
23
45
6�
1�
2�
3�
40
12
34
�2
�1
�4
�3
01
23
4�
10
12
34
56
7
�2
�1
�4
�3
01
23
4�
7�
6�
9�
8�
5�
4�
3�
2�
1
z� �
4
©G
lenc
oe/M
cGra
w-H
ill28
Gle
ncoe
Alg
ebra
2
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er o
r in
terv
aln
otat
ion
.Th
en,g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.8x
�6
�10
{x
x�
2} o
r [2
,∞)
2.23
�4u
�11
{u
u
3} o
r (3
,∞)
3.�
16 �
8r�
0 {r
r�
�2}
or
(�∞
,�2]
4.14
s�
9s�
5 {s
s�
1} o
r (�
∞,1
)
5.9x
�11
6x
�9 �x
x
�or �
,∞�
6.�
3(4w
�1)
18
�ww
��
�o
r ��
∞,�
�7.
1 �
8u�
3u�
10 {
uu
�1}
or
[1,∞
)8.
17.5
�19
�2.
5x{x
x�
0.6}
o
r (�
∞,0
.6)
9.9(
2r�
5) �
3 �
7r�
4 {r
r�
4}
10.1
�5(
x�
8) �
2 �
(x�
5) {
xx
�6}
o
r (�
∞,4
)o
r (�
∞,6
]
11.
��
3.5
{xx
��
1} o
r [�
1,∞
)12
.q�
2(2
�q)
�0 �q
q�
�or ��
∞,
�
13.�
36 �
2(w
�77
)
�4(
2w�
52)
14.4
n�
5(n
�3)
3(
n�
1) �
4 {w
w
�3}
or
(�3,
∞)
{nn
�4}
or
(�∞
,4)
Def
ine
a va
riab
le a
nd
wri
te a
n i
neq
ual
ity
for
each
pro
ble
m.T
hen
sol
ve.
15.T
wen
ty l
ess
than
a n
um
ber
is m
ore
than
tw
ice
the
sam
e n
um
ber.
n�
20
2n;
n�
�20
16.F
our
tim
es t
he
sum
of
twic
e a
nu
mbe
r an
d �
3 is
les
s th
an 5
.5 t
imes
th
at s
ame
nu
mbe
r.4[
2n�
(�3)
] �
5.5n
;n
�4.
8
17.H
OTE
LST
he
Lin
coln
’s h
otel
roo
m c
osts
$90
a n
igh
t.A
n a
ddit
ion
al 1
0% t
ax i
s ad
ded.
Hot
el p
arki
ng
is $
12 p
er d
ay.T
he
Lin
coln
’s e
xpec
t to
spe
nd
$30
in t
ips
duri
ng
thei
r st
ay.
Sol
ve t
he
ineq
ual
ity
90x
�90
(0.1
)x�
12x
�30
�60
0 to
fin
d h
ow m
any
nig
hts
th
eL
inco
ln’s
can
sta
y at
th
e h
otel
wit
hou
t ex
ceed
ing
tota
l h
otel
cos
ts o
f $6
00.
5 n
igh
ts
18.B
AN
KIN
GJa
n’s
acc
oun
t ba
lan
ce i
s $3
800.
Of
this
,$75
0 is
for
ren
t.Ja
n w
ants
to
keep
aba
lan
ce o
f at
lea
st $
500.
Wri
te a
nd
solv
e an
in
equ
alit
y de
scri
bin
g h
ow m
uch
sh
e ca
nw
ith
draw
an
d st
ill
mee
t th
ese
con
diti
ons.
3800
�75
0 �
w�
500;
w�
$255
0
0�
1�
21
23
45
6�
1�
2�
3�
40
12
34
0�
1�
2�
3�
41
23
4�
1�
2�
3�
40
12
34
4 � 34 � 3
4x�
3�
2
01
23
45
67
8�
2�
10
12
34
56
�2
�1
�4
�3
01
23
4�
1�
2�
3�
40
12
34
5 � 4�
2�
1�
4�
30
12
34
�1
�2
�3
�4
01
23
4
5 � 42 � 3
2 � 3
�2
�1
�4
�3
01
23
4�
2�
1�
4�
30
12
34
�1
�2
01
23
45
6�
1�
2�
3�
40
12
34
Pra
ctic
e (
Ave
rag
e)
So
lvin
g In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
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Kuta Software - Infinite Algebra 1 Name___________________________________
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Graphing Lines
Sketch the graph of each line.
1)
x
y
x
y
2)
x
y
x
y
3)
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7)
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y
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8)
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9)
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Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
© Glencoe/McGraw-Hill A11 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-4)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g L
inea
r E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill75
Gle
ncoe
Alg
ebra
2
Lesson 2-4
Form
s o
f Eq
uat
ion
s
Slo
pe-
Inte
rcep
t F
orm
o
f a
Lin
ear
Eq
uat
ion
y�
mx
�b,
whe
re m
is t
he s
lope
and
bis
the
y-in
terc
ept
Po
int-
Slo
pe
Fo
rm
y�
y 1�
m(x
�x 1
), w
here
(x 1
, y 1
) ar
e th
e co
ordi
nate
s of
a p
oint
on
the
line
and
of
a L
inea
r E
qu
atio
nm
is t
he s
lope
of
the
line
Wri
te a
n e
qu
atio
n i
nsl
ope-
inte
rcep
t fo
rm f
or t
he
lin
e th
ath
as s
lop
e �
2 an
d p
asse
s th
rou
gh t
he
poi
nt
(3,7
).
Su
bsti
tute
for
m,x
,an
d y
in t
he
slop
e-in
terc
ept
form
.y
�m
x�
bS
lope
-inte
rcep
t fo
rm
7 �
(�2)
(3)
�b
(x,
y)
�(3
, 7)
, m
��
2
7 �
�6
�b
Sim
plify
.
13 �
bA
dd 6
to
both
sid
es.
Th
e y-
inte
rcep
t is
13.
Th
e eq
uat
ion
in
sl
ope-
inte
rcep
t fo
rm i
s y
��
2x�
13.
Wri
te a
n e
qu
atio
n i
nsl
ope-
inte
rcep
t fo
rm f
or t
he
lin
e th
ath
as s
lop
e an
d x
-in
terc
ept
5.
y�
mx
�b
Slo
pe-in
terc
ept
form
0 �
��(5
) �
b(x
, y
) �
(5,
0),
m�
0 �
�b
Sim
plify
.
��
bS
ubtr
act
from
bot
h si
des.
Th
e y-
inte
rcep
t is
�.T
he
slop
e-in
terc
ept
form
is
y�
x�
.5 � 3
1 � 3
5 � 3
5 � 35 � 3
5 � 3
1 � 31 � 3
1 � 3
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
1.sl
ope
�2,
pass
es t
hro
ugh
(�
4,6)
2.sl
ope
,y-i
nte
rcep
t 4
y�
�2x
�2
y�
x�
4
3.sl
ope
1,pa
sses
th
rou
gh (
2,5)
4.sl
ope
�,p
asse
s th
rou
gh (
5,�
7)
y�
x�
3y
��
x�
6
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
5.6.
7.
y�
�3x
�9
y�
xy
�x
�1
4 � 91 � 9
5 � 4
x
y
O
( –4,
1)
( 5, 2
)
x
y O
( 4, 5
)
( 0, 0
)
x
y
O
( 1, 6
)
( 3, 0
)
13 � 513 � 5
3 � 23 � 2
©G
lenc
oe/M
cGra
w-H
ill76
Gle
ncoe
Alg
ebra
2
Para
llel a
nd
Per
pen
dic
ula
r Li
nes
Use
th
e sl
ope-
inte
rcep
t or
poi
nt-
slop
e fo
rm t
o fi
nd
equ
atio
ns
of l
ines
th
at a
re p
aral
lel
or p
erpe
ndi
cula
r to
a g
iven
lin
e.R
emem
ber
that
par
alle
lli
nes
hav
e eq
ual
slo
pe.T
he
slop
es o
f tw
o pe
rpen
dicu
lar
lin
es a
re n
egat
ive
reci
proc
als,
that
is,t
hei
r pr
odu
ct i
s �
1.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Wri
tin
g L
inea
r E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
Wri
te a
n e
qu
atio
n o
f th
eli
ne
that
pas
ses
thro
ugh
(8,
2) a
nd
is
per
pen
dic
ula
r to
th
e li
ne
wh
ose
equ
atio
n i
s y
��
x�
3.
Th
e sl
ope
of t
he
give
n l
ine
is �
.Sin
ce t
he
slop
es o
f pe
rpen
dicu
lar
lin
es a
re n
egat
ive
reci
proc
als,
the
slop
e of
th
e pe
rpen
dicu
lar
lin
e is
2.
Use
th
e sl
ope
and
the
give
n p
oin
t to
wri
teth
e eq
uat
ion
.y
� y
1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
2 �
2(x
�8)
(x1,
y1)
�(8
, 2)
, m
�2
y�
2 �
2x�
16D
istr
ibut
ive
Pro
p.
y�
2x�
14A
dd 2
to
each
sid
e.
An
equ
atio
n o
f th
e li
ne
is y
�2x
�14
.
1 � 2
1 � 2
Wri
te a
n e
qu
atio
n o
f th
eli
ne
that
pas
ses
thro
ugh
(�
1,5)
an
d i
sp
aral
lel
to t
he
grap
h o
f y
�3x
�1.
Th
e sl
ope
of t
he
give
n l
ine
is 3
.Sin
ce t
he
slop
es o
f pa
rall
el l
ines
are
equ
al,t
he
slop
eof
th
e pa
rall
el l
ine
is a
lso
3.U
se t
he
slop
e an
d th
e gi
ven
poi
nt
to w
rite
the
equ
atio
n.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
5 �
3(x
�(�
1))
(x1,
y1)
�(�
1, 5
), m
�3
y�
5 �
3x�
3D
istr
ibut
ive
Pro
p.
y�
3x�
8A
dd 5
to
each
sid
e.
An
equ
atio
n o
f th
e li
ne
is y
�3x
�8.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
1.pa
sses
th
rou
gh (
�4,
2),p
aral
lel
to t
he
lin
e w
hos
e eq
uat
ion
is
y�
x�
5y
�x
�4
2.pa
sses
th
rou
gh (
3,1)
,per
pen
dicu
lar
to t
he
grap
h o
f y
��
3x�
2y
�x
3.pa
sses
th
rou
gh (
1,�
1),p
aral
lel
to t
he
lin
e th
at p
asse
s th
rou
gh (
4,1)
an
d (2
,�3)
y�
2x�
3
4.pa
sses
th
rou
gh (
4,7)
,per
pen
dicu
lar
to t
he
lin
e th
at p
asse
s th
rou
gh (
3,6)
an
d (3
,15)
y�
7
5.pa
sses
th
rou
gh (
8,�
6),p
erpe
ndi
cula
r to
th
e gr
aph
of
2x�
y�
4y
��
x�
2
6.pa
sses
th
rou
gh (
2,�
2),p
erpe
ndi
cula
r to
th
e gr
aph
of
x�
5y�
6y
�5x
�12
7.pa
sses
th
rou
gh (
6,1)
,par
alle
l to
th
e li
ne
wit
h x
-in
terc
ept
�3
and
y-in
terc
ept
5
y�
x�
9
8.pa
sses
th
rou
gh (
�2,
1),p
erpe
ndi
cula
r to
th
e li
ne
y�
4x�
11y
��
x�
1 � 21 � 4
5 � 3
1 � 2
1 � 3
1 � 21 � 2
© Glencoe/McGraw-Hill A12 Glencoe Algebra 2
Answers (Lesson 2-4)
Skil
ls P
ract
ice
Wri
tin
g L
inea
r E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill77
Gle
ncoe
Alg
ebra
2
Lesson 2-4
Sta
te t
he
slop
e an
d y
-in
terc
ept
of t
he
grap
h o
f ea
ch e
qu
atio
n.
1.y
�7x
�5
7,�
52.
y�
�x
�3
�,3
3.y
�x
,04.
3x�
4y�
4�
,1
5.7y
�4x
�7
,�1
6.3x
�2y
�6
�0
,3
7.2x
�y
�5
2,�
58.
2y�
6 �
5x�
,3
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
9.10
.11
.
y�
3x�
1y
��
1y
��
2x�
3
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
12.s
lope
3,p
asse
s th
rou
gh (
1,�
3)13
.slo
pe �
1,pa
sses
th
rou
gh (
0,0)
y�
3x�
6y
��
x
14.s
lope
�2,
pass
es t
hro
ugh
(0,
�5)
15.s
lope
3,p
asse
s th
rou
gh (
2,0)
y�
�2x
�5
y�
3x�
6
16.p
asse
s th
rou
gh (
�1,
�2)
an
d (�
3,1)
17.p
asse
s th
rou
gh (
�2,
�4)
an
d (1
,8)
y�
�x
�y
�4x
�4
18.x
-in
terc
ept
2,y-
inte
rcep
t �
619
.x-i
nte
rcep
t ,y
-in
terc
ept
5
y�
3x�
6y
��
2x�
5
20.p
asse
s th
rou
gh (
3,�
1),p
erpe
ndi
cula
r to
th
e gr
aph
of
y�
�x
�4.
y�
3x�
101 � 3
5 � 2
7 � 23 � 2
x
y
O
( 0, 3
)
( 3, –
3)
x
y
O( –
3, –
1)( 4
, –1)
x
y
O
( –1,
–4)
( 1, 2
)
5 � 2
3 � 24 � 7
3 � 42 � 3
2 � 3
3 � 53 � 5
©G
lenc
oe/M
cGra
w-H
ill78
Gle
ncoe
Alg
ebra
2
Sta
te t
he
slop
e an
d y
-in
terc
ept
of t
he
grap
h o
f ea
ch e
qu
atio
n.
1.y
�8x
�12
8,12
2.y
�0.
25x
�1
0.25
,�1
3.y
��
x�
,0
4.3y
�7
0,5.
3x�
�15
�5y
,36.
2x�
3y�
10,�
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
7.8.
9.
y�
2y
�x
�2
y�
�x
�1
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
10.s
lope
�5,
pass
es t
hro
ugh
(�
3,�
8)11
.slo
pe
,pas
ses
thro
ugh
(10
,�3)
y�
�5x
�23
y�
x�
11
12.s
lope
0,p
asse
s th
rou
gh (
0,�
10)
13.s
lope
�,p
asse
s th
rou
gh (
6,�
8)
y�
�10
y�
�x
�4
14.p
asse
s th
rou
gh (
3,11
) an
d (�
6,5)
15.p
asse
s th
rou
gh (
7,�
2) a
nd
(3,�
1)
y�
x�
9y
��
x�
16.x
-in
terc
ept
3,y-
inte
rcep
t 2
17.x
-in
terc
ept
�5,
y-in
terc
ept
7
y�
�x
�2
y�
x�
7
18.p
asse
s th
rou
gh (
�8,
�7)
,per
pen
dicu
lar
to t
he
grap
h o
f y
�4x
�3
y�
�x
�9
19.R
ESER
VO
IRS
Th
e su
rfac
e of
Gra
nd
Lak
e is
at
an e
leva
tion
of
648
feet
.Du
rin
g th
ecu
rren
t dr
ough
t,th
e w
ater
lev
el i
s dr
oppi
ng
at a
rat
e of
3 i
nch
es p
er d
ay.I
f th
is t
ren
dco
nti
nu
es,w
rite
an
equ
atio
n t
hat
giv
es t
he
elev
atio
n i
n f
eet
of t
he
surf
ace
of G
ran
d L
ake
afte
r x
days
.y
��
0.25
x�
648
20.B
USI
NES
ST
ony
Mar
con
i’s c
ompa
ny
man
ufa
ctu
res
CD
-RO
M d
rive
s.T
he
com
pan
y w
ill
mak
e $1
50,0
00 p
rofi
t if
it
man
ufa
ctu
res
100,
000
driv
es,a
nd
$1,7
50,0
00 p
rofi
t if
it
man
ufa
ctu
res
500,
000
driv
es.T
he
rela
tion
ship
bet
wee
n t
he
nu
mbe
r of
dri
ves
man
ufa
ctu
red
and
the
prof
it i
s li
nea
r.W
rite
an
equ
atio
n t
hat
giv
es t
he
prof
it P
wh
en
ndr
ives
are
man
ufa
ctu
red.
P�
4n�
250,
000
1 � 4
7 � 52 � 3
1 � 41 � 4
2 � 3
2 � 32 � 3
4 � 54 � 5
2 � 33 � 2
x
y
O( 3
, –1)
( –3,
3)
x
y
O
( 4, 4
)
( 0, –
2)
x
y
O
( 0, 2
)
10 � 32 � 3
3 � 57 � 3
3 � 53 � 5
Pra
ctic
e (
Ave
rag
e)
Wri
tin
g L
inea
r E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
© Glencoe/McGraw-Hill A14 Glencoe Algebra 2
Answers (Lesson 2-5)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill81
Gle
ncoe
Alg
ebra
2
Lesson 2-5
Scat
ter
Plo
tsW
hen
a s
et o
f da
ta p
oin
ts i
s gr
aph
ed a
s or
dere
d pa
irs
in a
coo
rdin
ate
plan
e,th
e gr
aph
is
call
ed a
sca
tter
plo
t.A
sca
tter
plo
t ca
n b
e u
sed
to d
eter
min
e if
th
ere
isa
rela
tion
ship
am
ong
the
data
.
BA
SEB
ALL
Th
e ta
ble
bel
ow s
how
s th
e n
um
ber
of
hom
e ru
ns
and
run
s b
atte
d i
n f
or v
ario
us
bas
ebal
l p
laye
rs w
ho
won
th
e M
ost
Val
uab
le P
laye
rA
war
d d
uri
ng
the
1990
s.M
ake
a sc
atte
r p
lot
of t
he
dat
a.
Sour
ce:N
ew Y
ork
Times
Alm
anac
Mak
e a
scat
ter
plo
t fo
r th
e d
ata
in e
ach
tab
le b
elow
.
1.FU
EL E
FFIC
IEN
CY
Th
e ta
ble
belo
w s
how
s th
e av
erag
e fu
el e
ffic
ien
cy i
n m
iles
per
gal
lon
of
new
car
s m
anu
fact
ure
d du
rin
g th
e ye
ars
list
ed.
Sour
ce:N
ew Y
ork
Times
Alm
anac
2.C
ON
GR
ESS
Th
e ta
ble
belo
w s
how
s th
e n
um
ber
of
wom
en s
ervi
ng
in t
he
Un
ited
Sta
tes
Con
gres
s du
rin
g th
e ye
ars
1987
�19
99.
Sour
ce:W
all S
treet
Jour
nal A
lman
ac
Co
ng
ress
ion
al S
essi
on
Nu
mb
er o
f Wo
men
100
25
101
31
102
33
103
55
104
58
105
62
Sess
ion
of
Co
ng
ress
Number of Women
100
102
104
70 56 42 28 14 0
Wo
men
in
Co
ng
ress
Year
Fu
el E
ffic
ien
cy (
mp
g)
1960
15.5
1970
14.1
1980
22.6
1990
26.9
Year
Miles per Gallon
1960
1970
1980
1990
36 30 24 18 12 6 0Avera
ge F
uel
Eff
icie
ncy
Ho
me
Ru
ns
MV
P H
Rs
an
d R
BIs
Runs Batted In
126
024
3618
3042
48
150
125
100 75 50 25
Ho
me
Ru
ns
Ru
ns
Bat
ted
In
3311
4
3911
6
4013
0
2861
4112
8
4714
4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill82
Gle
ncoe
Alg
ebra
2
Pred
icti
on
Eq
uat
ion
sA
lin
e of
fit
is a
lin
e th
at c
lose
ly a
ppro
xim
ates
a s
et o
f da
tagr
aph
ed i
n a
sca
tter
plo
t.T
he
equ
atio
n o
f a
lin
e of
fit
is
call
ed a
pre
dic
tion
eq
uat
ion
beca
use
it
can
be
use
d to
pre
dict
val
ues
not
giv
en i
n t
he
data
set
.
To
fin
d a
pred
icti
on e
quat
ion
for
a s
et o
f da
ta,s
elec
t tw
o po
ints
th
at s
eem
to
repr
esen
t th
eda
ta w
ell.
Th
en t
o w
rite
th
e pr
edic
tion
equ
atio
n,u
se w
hat
you
kn
ow a
bou
t w
riti
ng
a li
nea
req
uat
ion
wh
en g
iven
tw
o po
ints
on
th
e li
ne.
STO
RA
GE
CO
STS
Acc
ord
ing
to a
cer
tain
pre
dic
tion
eq
uat
ion
,th
eco
st o
f 20
0 sq
uar
e fe
et o
f st
orag
e sp
ace
is $
60.T
he
cost
of
325
squ
are
feet
of
stor
age
spac
e is
$16
0.
a.F
ind
th
e sl
ope
of t
he
pre
dic
tion
eq
uat
ion
.Wh
at d
oes
it r
epre
sen
t?S
ince
th
e co
st d
epen
ds u
pon
th
e sq
uar
e fo
otag
e,le
t x
repr
esen
t th
e am
oun
t of
sto
rage
spac
e in
squ
are
feet
an
d y
repr
esen
t th
e co
st i
n d
olla
rs.T
he
slop
e ca
n b
e fo
un
d u
sin
g th
e
form
ula
m�
.So,
m�
��
0.8
Th
e sl
ope
of t
he
pred
icti
on e
quat
ion
is
0.8.
Th
is m
ean
s th
at t
he
pric
e of
sto
rage
in
crea
ses
80¢
for
each
on
e-sq
uar
e-fo
ot i
ncr
ease
in
sto
rage
spa
ce.
b.
Fin
d a
pre
dic
tion
eq
uat
ion
.U
sin
g th
e sl
ope
and
one
of t
he
poin
ts o
n t
he
lin
e,yo
u c
an u
se t
he
poin
t-sl
ope
form
to
fin
da
pred
icti
on e
quat
ion
.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
60 �
0.8(
x�
200)
(x1,
y1)
�(2
00,
60),
m�
0.8
y�
60 �
0.8x
�16
0D
istr
ibut
ive
Pro
pert
y
y�
0.8x
�10
0A
dd 6
0 to
bot
h si
des.
A p
redi
ctio
n e
quat
ion
is
y�
0.8x
�10
0.
SALA
RIE
ST
he
tab
le b
elow
sh
ows
the
year
s of
exp
erie
nce
for
eig
ht
tech
nic
ian
s at
Lew
is T
ech
omat
ic a
nd
th
e h
ourl
y ra
te o
f p
ay e
ach
tec
hn
icia
n e
arn
s.U
se t
he
dat
afo
r E
xerc
ises
1 a
nd
2.
Exp
erie
nce
(ye
ars)
94
31
106
128
Ho
url
y R
ate
of
Pay
$17
$10
$10
$7$1
9$1
2$2
0$1
5
1.D
raw
a s
catt
er p
lot
to s
how
how
yea
rs o
f ex
peri
ence
are
re
late
d to
hou
rly
rate
of
pay.
Dra
w a
lin
e of
fit
.S
ee g
rap
h.
2.W
rite
a p
redi
ctio
n e
quat
ion
to
show
how
yea
rs o
f ex
peri
ence
(x)
are
rela
ted
to h
ourl
y ra
te o
f pa
y (y
).S
amp
le a
nsw
eru
sin
g (
1,7)
an
d (
9,17
):y
�1.
25x
�5.
75
Exp
erie
nce
(ye
ars)
Hourly Pay ($)
20
610
48
1214
24 20 16 12 8 4
Tech
nic
ian
Sala
ries
100
� 125
160
�60
��
325
�20
0y 2
�y 1
� x 2�
x 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-5)
Skil
ls P
ract
ice
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill83
Gle
ncoe
Alg
ebra
2
Lesson 2-5
For
Exe
rcis
es 1
–3,c
omp
lete
par
ts a
–c f
or e
ach
set
of
dat
a.
a.D
raw
a s
catt
er p
lot.
b.
Use
tw
o or
der
ed p
airs
to
wri
te a
pre
dic
tion
eq
uat
ion
.c.
Use
you
r p
red
icti
on e
qu
atio
n t
o p
red
ict
the
mis
sin
g va
lue.
1.1a
.
1b.
Sam
ple
an
swer
usi
ng
(1,
1) a
nd
(8,
15):
y�
2x�
11c
.S
amp
le a
nsw
er:
19
2.2a
.
2b.
Sam
ple
an
swer
usi
ng
(5,
9) a
nd
(40
,44)
:y
�x
�4
2c.
Sam
ple
an
swer
:54
3.3a
.
3b.
Sam
ple
an
swer
usi
ng
(2,
16)
and
(7,
34):
y�
3.6x
�8.
83c
.S
amp
le a
nsw
er:
19.6
13
57
24
68
36 30 24 18 12 6 0x
yx
y
116
216
3?
422
530
734
836
515
2535
1020
3040
40 32 24 16 8 0x
yx
y
59
1017
2022
2530
3538
4044
50?
13
57
24
68
15 12 9 6 3 0x
yx
y
11
35
47
611
712
815
10?
©G
lenc
oe/M
cGra
w-H
ill84
Gle
ncoe
Alg
ebra
2
For
Exe
rcis
es 1
–3,c
omp
lete
par
ts a
–c f
or e
ach
set
of
dat
a.a.
Dra
w a
sca
tter
plo
t.b
.U
se t
wo
ord
ered
pai
rs t
o w
rite
a p
red
icti
on e
qu
atio
n.
c.U
se y
our
pre
dic
tion
eq
uat
ion
to
pre
dic
t th
e m
issi
ng
valu
e.
1.FU
EL E
CO
NO
MY
Th
e ta
ble
give
s th
e ap
prox
imat
e w
eigh
ts i
n t
ons
and
esti
mat
es
for
over
all
fuel
eco
nom
y in
mil
es p
er g
allo
n
for
seve
ral
cars
.1b
.Sam
ple
an
swer
usi
ng
(1.
4,24
) an
d
(2.4
,15)
:y
��
9x�
36.6
1c.S
amp
le a
nsw
er:
18.6
mi/g
al
2.A
LTIT
UD
EIn
mos
t ca
ses,
tem
pera
ture
dec
reas
es w
ith
in
crea
sin
g al
titu
de.A
s A
nch
ara
driv
es i
nto
th
e m
oun
tain
s,h
er c
ar t
her
mom
eter
reg
iste
rs t
he
tem
pera
ture
s (°
F)
show
nin
th
e ta
ble
at t
he
give
n a
ltit
ude
s (f
eet)
.
2b.S
amp
le a
nsw
er u
sin
g (
7500
,61)
an
d
(970
0,50
):y
��
0.00
5x�
98.5
2c.S
amp
le a
nsw
er:
38.5
°F
3.H
EALT
HA
lton
has
a t
read
mil
l th
at u
ses
the
tim
e on
th
e tr
eadm
ill
and
the
spee
d of
w
alki
ng
or r
un
nin
g to
est
imat
e th
e n
um
ber
of C
alor
ies
he
burn
s du
rin
g a
wor
kou
t.T
he
tabl
e gi
ves
wor
kou
t ti
mes
an
d C
alor
ies
burn
ed f
or s
ever
al w
orko
uts
.
3b.S
amp
le a
nsw
er u
sin
g (
24,2
80)
and
(48,
440)
:y
�6.
67x
�11
9.92
3c.S
amp
le a
nsw
er:
abo
ut
520
calo
ries
Tim
e (m
in)
Calories Burned
010
2030
4050
555
1525
3545
500
400
300
200
100
Bu
rnin
g C
alo
ries
Tim
e (m
in)
1824
3040
4248
5260
Cal
ori
es B
urn
ed26
028
032
038
040
044
047
5?
Alt
itu
de
(ft)
Temperature (�F)
07,
000
8,00
09,
000
10,0
00
65 60 55 50 45
Tem
pera
ture
Vers
us
Alt
itu
de
Alt
itu
de
(ft)
7500
8200
8600
9200
9700
10,4
0012
,000
Tem
per
atu
re (
�F)
6158
5653
5046
?
Wei
gh
t (t
on
s)
Fuel Economy (mi/gal)
00.
51.
01.
52.
02.
5
30 25 20 15 10 5Fuel
Eco
no
my V
ers
us
Weig
ht
Wei
gh
t (t
on
s)1.
31.
41.
51.
82
2.1
2.4
Mile
s p
er G
allo
n29
2423
21?
1715
Pra
ctic
e (
Ave
rag
e)
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
© Glencoe/McGraw-Hill A2 Glencoe Algebra 2
Answers (Lesson 2-1)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Rel
atio
ns
and
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
©G
lenc
oe/M
cGra
w-H
ill57
Gle
ncoe
Alg
ebra
2
Lesson 2-1
Gra
ph
Rel
atio
ns
A r
elat
ion
can
be
repr
esen
ted
as a
set
of
orde
red
pair
s or
as
aneq
uat
ion
;th
e re
lati
on i
s th
en t
he
set
of a
ll o
rder
ed p
airs
(x,
y) t
hat
mak
e th
e eq
uat
ion
tru
e.T
he
dom
ain
of a
rel
atio
n i
s th
e se
t of
all
fir
st c
oord
inat
es o
f th
e or
dere
d pa
irs,
and
the
ran
geis
th
e se
t of
all
sec
ond
coor
din
ates
.A
fu
nct
ion
is a
rel
atio
n i
n w
hic
h e
ach
ele
men
t of
th
e do
mai
n i
s pa
ired
wit
h e
xact
ly o
ne
elem
ent
of t
he
ran
ge.Y
ou c
an t
ell
if a
rel
atio
n i
s a
fun
ctio
n b
y gr
aph
ing,
then
usi
ng
the
vert
ical
lin
e te
st.I
f a
vert
ical
lin
e in
ters
ects
th
e gr
aph
at
mor
e th
an o
ne
poin
t,th
ere
lati
on i
s n
ot a
fu
nct
ion
.
Gra
ph
th
e eq
uat
ion
y�
2x�
3 an
d f
ind
th
e d
omai
n a
nd
ran
ge.D
oes
the
equ
atio
n r
epre
sen
t a
fun
ctio
n?
Mak
e a
tabl
e of
val
ues
to
fin
d or
dere
d pa
irs
that
sa
tisf
y th
e eq
uat
ion
.Th
en g
raph
th
e or
dere
d pa
irs.
Th
e do
mai
n a
nd
ran
ge a
re b
oth
all
rea
l n
um
bers
.Th
egr
aph
pas
ses
the
vert
ical
lin
e te
st,s
o it
is
fun
ctio
n.
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
.Th
en d
eter
min
ew
het
her
th
e re
lati
on o
r eq
uat
ion
is
a fu
nct
ion
.
1.{(
1,3)
,(�
3,5)
,2.
{(3,
�4)
,(1,
0),
3.{(
0,4)
,(�
3,�
2),
(�2,
5),(
2,3)
}(2
,�2)
,(3,
2)}
(3,2
),(5
,1)}
D �
{�3,
�2,
1,2}
,D
�{1
,2,3
},D
�{�
3,0,
3,5}
,R
�{3
,5};
yes
R �
{�4,
�2,
0,2}
;n
oR
�{�
2,1,
2,4}
;ye
s
4.y
�x2
�1
5.y
�x
�4
6.y
�3x
�2
D �
all r
eals
,D
�al
l rea
ls,
D �
all r
eals
,R
�{y
y�
�1}
;ye
sR
�al
l rea
ls;
yes
R �
all r
eals
;ye
sx
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
xy
�1
�5
0�
3
1�
1
21
33
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill58
Gle
ncoe
Alg
ebra
2
Equ
atio
ns
of
Fun
ctio
ns
and
Rel
atio
ns
Equ
atio
ns
that
rep
rese
nt
fun
ctio
ns
are
ofte
n w
ritt
en i
n f
un
ctio
nal
not
atio
n.F
or e
xam
ple,
y�
10 �
8xca
n b
e w
ritt
en a
s f(
x) �
10 �
8x.T
his
not
atio
n e
mph
asiz
es t
he
fact
th
at t
he
valu
es o
f y,
the
dep
end
ent
vari
able
,dep
end
on t
he
valu
es o
f x,
the
ind
epen
den
t va
riab
le.
To
eval
uat
e a
fun
ctio
n,o
r fi
nd
a fu
nct
ion
al v
alu
e,m
ean
s to
su
bsti
tute
a g
iven
val
ue
in t
he
dom
ain
in
to t
he
equ
atio
n t
o fi
nd
the
corr
espo
ndi
ng
elem
ent
in t
he
ran
ge.
Giv
en t
he
fun
ctio
n f
(x)
�x2
�2x
,fin
d e
ach
val
ue.
a.f(
3)
f(x)
�x2
�2x
Orig
inal
fun
ctio
n
f(3)
�32
�2(
3)S
ubst
itute
.
�15
Sim
plify
.
b.
f(5a
)
f(x)
�x2
�2x
Orig
inal
fun
ctio
n
f(5a
) �
(5a)
2�
2(5a
)S
ubst
itute
.
�25
a2�
10a
Sim
plify
.
Fin
d e
ach
val
ue
if f
(x)
��
2x�
4.
1.f(
12)
�20
2.f(
6)�
83.
f(2b
)�
4b�
4
Fin
d e
ach
val
ue
if g
(x)
�x3
�x.
4.g(
5)12
05.
g(�
2)�
66.
g(7c
)34
3c3
�7c
Fin
d e
ach
val
ue
if f
(x)
�2x
�an
d g
(x)
�0.
4x2
�1.
2.
7.f(
0.5)
58.
f(�
8)�
169.
g(3)
2.4
10.g
(�2.
5)1.
311
.f(4
a)8a
�12
.g�
��
1.2
13.f
��6
14.g
(10)
38.8
15.f
(200
)40
0.01
Let
f(x
) �
2x2
�1.
16.F
ind
the
valu
es o
f f(
2) a
nd
f(5)
.f(
2) �
7,f(
5) �
49
17.C
ompa
re t
he
valu
es o
f f(
2) �
f(5)
an
d f(
2 �
5).
f(2)
�f(
5) �
343,
f(2
�5)
�19
9
2 � 31 � 3
b2
� 10b � 2
1 � 2a1 � 4
2 � x
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Rel
atio
ns
and
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-1)
Skil
ls P
ract
ice
Rel
atio
ns
and
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
©G
lenc
oe/M
cGra
w-H
ill59
Gle
ncoe
Alg
ebra
2
Lesson 2-1
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.W
rite
yes
or n
o.
1.ye
s2.
no
3.ye
s4.
no
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
.Th
en d
eter
min
ew
het
her
th
e re
lati
on o
r eq
uat
ion
is
a fu
nct
ion
.
5.{(
2,�
3),(
2,4)
,(2,
�1)
}6.
{(2,
6),(
6,2)
}
D �
{2},
R �
{�3,
�1,
4};
no
D �
{2,6
},R
�{2
,6};
yes
7.{(
�3,
4),(
�2,
4),(
�1,
�1)
,(3,
�1)
}8.
x�
�2
D �
{�3,
�2,
�1,
3},
D �
{�2}
,R �
all r
eals
;n
o
R �
{�1,
4};
yes
Fin
d e
ach
val
ue
if f
(x)
�2x
�1
and
g(x
) �
2 �
x2.
9.f(
0)�
110
.f(1
2)23
11.g
(4)
�14
12.f
(�2)
�5
13.g
(�1)
114
.f(d
)2d
�1
x
y
O
( –2,
4)
( –3,
4)
( –1,
–1)
( 3, –
1)x
y
O
( 2, 6
) ( 6, 2
)
x
y
O
( 2, 4
)
( 2, –
1)
( 2, –
3)
x
y
O
x
y
O
xy
12
24
36
D 3
R 1 5
D 100
200
300
R 50
100
150
©G
lenc
oe/M
cGra
w-H
ill60
Gle
ncoe
Alg
ebra
2
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.W
rite
yes
or n
o.
1.n
o2.
yes
3.ye
s4.
no
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
.Th
en d
eter
min
ew
het
her
th
e re
lati
on o
r eq
uat
ion
is
a fu
nct
ion
.
5.{(
�4,
�1)
,(4,
0),(
0,3)
,(2,
0)}
6.y
�2x
�1
D �
{�4,
0,2,
4},
D �
all r
eals
,R �
all r
eals
;ye
sR
�{�
1,0,
3};
yes
Fin
d e
ach
val
ue
if f
(x)
�an
d g
(x)
��
2x�
3.
7.f(
3)1
8.f(
�4)
�9.
g ��2
10.f
(�2)
un
def
ined
11.g
(�6)
1512
.f(m
�2)
13.M
USI
CT
he
orde
red
pair
s (1
,16)
,(2,
16),
(3,3
2),(
4,32
),an
d (5
,48)
rep
rese
nt
the
cost
of
buyi
ng
vari
ous
nu
mbe
rs o
f C
Ds
thro
ugh
a m
usi
c cl
ub.
Iden
tify
th
e do
mai
n a
nd
ran
ge o
fth
e re
lati
on.I
s th
e re
lati
on a
fu
nct
ion
?D
�{1
,2,3
,4,5
},R
�{1
6,32
,48}
;ye
s
14.C
OM
PUTI
NG
If a
com
pute
r ca
n d
o on
e ca
lcu
lati
on i
n 0
.000
0000
015
seco
nd,
then
th
efu
nct
ion
T(n
) �
0.00
0000
0015
ngi
ves
the
tim
e re
quir
ed f
or t
he
com
pute
r to
do
nca
lcu
lati
ons.
How
lon
g w
ould
it
take
th
e co
mpu
ter
to d
o 5
bill
ion
cal
cula
tion
s?7.
5 s
5 � m
1 � 25 � 2
5� x
�2
x
y
O
( –4,
–1)
( 2, 0
)
( 0, 3
)
( 4, 0
) x
y
O
x
y
O
xy
�3
0
�1
�1
00
2�
2
34
D 5 10 15
R 105
110
D 2 8
R 21 25 30
Pra
ctic
e (
Ave
rag
e)
Rel
atio
ns
and
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
2-1
2-1
