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Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
3
Gle
ncoe A
lgeb
ra 1
An
tici
pati
on
Gu
ide
An
aly
zin
g L
inear
Eq
uati
on
s
B
efo
re y
ou
beg
in C
ha
pte
r 4
•
R
ead
each
sta
tem
en
t.
•
D
eci
de w
heth
er
you
Agre
e (
A)
or
Dis
agre
e (
D)
wit
h t
he s
tate
men
t.
•
W
rite
A o
r D
in
th
e f
irst
colu
mn
OR
if
you
are
not
sure
wh
eth
er
you
agre
e o
r d
isagre
e,
wri
te N
S (
Not
Su
re).
A
fter y
ou
com
ple
te C
ha
pte
r 4
•
R
ere
ad
each
sta
tem
en
t an
d c
om
ple
te t
he l
ast
colu
mn
by e
nte
rin
g a
n A
or
a D
.
•
D
id a
ny o
f you
r op
inio
ns
abou
t th
e s
tate
men
ts c
han
ge f
rom
th
e f
irst
colu
mn
?
•
F
or
those
sta
tem
en
ts t
hat
you
mark
wit
h a
D,
use
a p
iece
of
pap
er
to w
rite
an
exam
ple
of
wh
y y
ou
dis
agre
e.
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Th
e s
lop
e o
f a l
ine g
iven
by a
n e
qu
ati
on
in
th
e f
orm
y =
mx +
b
can
be d
ete
rmin
ed
by l
ook
ing a
t th
e e
qu
ati
on
.A
2.
Th
e y
-in
terc
ep
t of
y =
12
x -
8 i
s 8.
D 3.
If t
wo p
oin
ts o
n a
lin
e a
re k
now
n,
then
an
equ
ati
on
can
be
wri
tten
for
that
lin
e.
A
4.
An
equ
ati
on
in
th
e f
orm
y =
mx +
b i
s in
poin
t-sl
op
e f
orm
.D
5.
If a
pair
of
lin
es
are
para
llel,
th
en
th
ey h
ave t
he s
am
e s
lop
e.
A 6.
Lin
es
that
inte
rsect
at
righ
t an
gle
s are
call
ed
perp
en
dic
ula
r
lin
es.
A
7.
A s
catt
er
plo
t is
said
to h
ave a
negati
ve c
orr
ela
tion
wh
en
th
e
poin
ts a
re r
an
dom
an
d s
how
no r
ela
tion
betw
een
x a
nd
y.
D
8.
Th
e c
lose
r th
e c
orr
ela
tion
coeff
icie
nt
is t
o z
ero
, th
e m
ore
clo
sely
a b
est
-fit
lin
e m
od
els
a s
et
of
data
.D
9.
Th
e e
qu
ati
on
s of
a r
egre
ssio
n l
ine a
nd
a m
ed
ian
-fit
lin
e a
re
very
sim
ilar.
A
10.
Ste
p f
un
ctio
ns
an
d a
bso
lute
valu
e f
un
ctio
ns
are
typ
es
of
pie
cew
ise-l
inear
fun
ctio
ns.
A
4 Ste
p 1
Ste
p 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-1
Ch
ap
ter
4
5
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Slo
pe-I
nte
rcep
t Fo
rm
Slo
pe-I
nte
rcep
t F
orm
y =
mx +
b,
where
m is t
he g
iven s
lope a
nd b
is t
he y
-inte
rcept
W
rit
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine w
ith
a s
lop
e
of -
4 a
nd
a y
-in
tercep
t o
f 3.
y =
mx +
b
Slo
pe-inte
rcept
form
y =
-4
x +
3
Repla
ce m
with -
4 a
nd b
with 3
.
G
ra
ph
3x
- 4
y =
8.
3x -
4y =
8
Origin
al equation
-
4y =
-3
x +
8
Subtr
act
3x f
rom
each s
ide.
-
4y
−
-4
= -
3x +
8
−
-4
D
ivid
e e
ach s
ide b
y -
4.
y =
3
−
4 x
- 2
S
implif
y.
Th
e y
-in
terc
ep
t of
y =
3
−
4 x
- 2
is
-2 a
nd
th
e s
lop
e i
s 3
−
4 .
So g
rap
h t
he p
oin
t (0
, -
2).
Fro
m
this
poin
t, m
ove u
p 3
un
its
an
d r
igh
t 4 u
nit
s. D
raw
a l
ine p
ass
ing t
hro
ugh
both
poin
ts.
Exerc
ises
Writ
e a
n e
qu
ati
on
of
a l
ine i
n s
lop
e-i
nte
rcep
t fo
rm
wit
h t
he g
iven
slo
pe a
nd
y-i
nte
rcep
t.
1. sl
op
e:
8,
y-i
nte
rcep
t -
3
2. sl
op
e:
-2,
y-i
nte
rcep
t -
1
3. sl
op
e:
-1,
y-i
nte
rcep
t -
7
y
= 8
x -
3
y =
-2x -
1
y =
-x -
7
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r e
ach
gra
ph
sh
ow
n.
4.
( 0,
–2
)
( 1,
0)
x
y
O
5.
( 3,
0)
( 0,
3)
x
y
O
6.
( 4,
–2
)
( 0,
–5)
x
y
O
y
= 2
x -
2
y =
-x +
3
y =
3 −
4 x
- 5
Gra
ph
ea
ch
eq
ua
tio
n.
7. y =
2x +
1
8. y =
-3
x +
2
9. y =
-x -
1
x
y
O
x
y
O
x
y
O
( 0,
–2)
( 4,
1)
x
y
O
3x
- 4
y=
8
4-1
Exam
ple
1
Exam
ple
2
Answers (Anticipation Guide and Lesson 4-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
6
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Mo
delin
g R
eal-
Wo
rld
Data
MED
IA S
ince 1
999,
the n
um
ber o
f m
usic
ca
ssett
es s
old
ha
s
decrea
sed
by
an
av
era
ge r
ate
of
27 m
illi
on
per y
ea
r.
Th
ere w
ere 1
24 m
illi
on
mu
sic
ca
ssett
es s
old
in
1999.
a.
Writ
e a
lin
ea
r e
qu
ati
on
to
fin
d t
he a
vera
ge n
um
ber o
f m
usic
ca
ssett
es s
old
in
an
y y
ea
r a
fter 1
999.
Th
e ra
te o
f ch
an
ge
is -
27 m
illi
on p
er y
ear.
In
th
e fi
rst
yea
r, t
he
nu
mber
of
mu
sic
cass
ette
s so
ld w
as
124 m
illi
on.
Let
N =
th
e n
um
ber
of
mil
lion
s of
mu
sic
cass
ette
s so
ld.
Let
x =
th
e n
um
ber
of
yea
rs a
fter
1999.
An
equ
ati
on i
s N
= -
27
x +
124.
b.
Gra
ph
th
e e
qu
ati
on
.
Th
e gra
ph
of
N =
-27x +
124 i
s a l
ine
that
pass
es
thro
ugh
th
e p
oin
t at
(0,
124)
an
d h
as
a s
lop
e of
-27.
c.
Fin
d t
he a
pp
ro
xim
ate
nu
mb
er o
f m
usic
ca
ssett
es
so
ld i
n 2
003.
N =
-27x +
124
Origin
al equation
N =
-27(4
) +
124
Repla
ce x
with 3
.
N =
16
S
implif
y.
Th
ere
wer
e abou
t 16 m
illi
on m
usi
c ca
sset
tes
sold
in
2003.
Exerc
ises
1. M
USIC
In
2001,
full
-len
gth
cass
ette
s re
pre
sen
ted
3.4
% o
f to
tal
mu
sic
sale
s. B
etw
een
2001 a
nd
2006,
the
per
cen
t d
ecre
ase
d b
y a
bou
t 0.5
% p
er y
ear.
a.
Wri
te a
n e
qu
ati
on t
o fi
nd
th
e p
erce
nt
P o
f re
cord
ed m
usi
c so
ld a
s fu
ll-l
ength
cass
ette
s fo
r an
y y
ear
x b
etw
een
2001 a
nd
2006.
b.
Gra
ph
th
e eq
uati
on o
n t
he
gri
d a
t th
e ri
gh
t.
c.
Fin
d t
he
per
cen
t of
rec
ord
ed m
usi
c so
ld
as
full
-len
gth
cass
ette
s in
2004.
2. PO
PU
LA
TIO
N T
he
pop
ula
tion
of
the
Un
ited
Sta
tes
is
pro
ject
ed t
o be
300 m
illi
on b
y t
he
yea
r 2010.
Bet
wee
n
2010 a
nd
2050,
the
pop
ula
tion
is
exp
ecte
d t
o in
crea
se
by a
bou
t 2.5
mil
lion
per
yea
r.
a.
Wri
te a
n e
qu
ati
on t
o fi
nd
th
e p
opu
lati
on P
in
an
y y
ear
x
bet
wee
n 2
010 a
nd
2050.
b.
Gra
ph
th
e eq
uati
on o
n t
he
gri
d a
t th
e ri
gh
t.
c.
Fin
d t
he
pop
ula
tion
in
2050.
ab
ou
t 400,0
00,0
00
Full
-len
gth
Cas
sett
e Sa
les
Percent of Total Music Sales
1.5
%
2.0
%
1.0
%
2.5
%
3.0
%
3.5
%
Yea
rs S
ince
200
1
32
10
54
Sou
rce:
RIA
A
Pro
ject
ed U
nit
edSt
ates
Po
pu
lati
on
Yea
rs S
ince
201
0
Population (millions)
020
40
x
P
400
380
360
340
320
300
Sou
rce:
The W
orld A
lmanac
Mu
sic
Cas
sett
es S
old
Number of Cassettes
50
75
25 0
100
125
Yea
rs S
ince
199
9
32
15
74
6
Sou
rce:
The W
orld A
lmanac
4-1 Exam
ple
P =
-0.5
x +
3.4 1.9
%
P =
2,5
00,0
00x +
300,0
00,0
00
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-1
Ch
ap
ter
4
7
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rmW
rit
e a
n e
qu
ati
on
of
a l
ine i
n s
lop
e-i
nte
rcep
t fo
rm
wit
h t
he g
iven
slo
pe
an
d y
-in
tercep
t.
1. sl
ope:
5,
y-i
nte
rcep
t: -
3 y =
5x -
3
2. sl
ope:
-2,
y-i
nte
rcep
t: 7
y =
-2x +
7
3. sl
ope:
-6,
y-i
nte
rcep
t: -
2 y
= -
6x -
2
4. sl
ope:
7,
y-i
nte
rcep
t: 1
y =
7x +
1
5. sl
ope:
3,
y-i
nte
rcep
t: 2
y =
3x +
2
6. sl
ope:
-4,
y-i
nte
rcep
t: -
9 y
= -
4x -
9
7. sl
ope:
1,
y-i
nte
rcep
t: -
12 y
= x
- 1
2
8. sl
ope:
0,
y-i
nte
rcep
t: 8
y =
8
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r e
ach
gra
ph
sh
ow
n.
9.
( 2,
1)
( 0,
–3
)
x
y
O
10.
( 0,
2)
( 2,
–4
)
x
y
O
11.
( 0,
–1
)
( 2,
–3)x
y O
y
= 2
x -
3
y =
-3
x +
2
y =
-x -
1
Gra
ph
ea
ch
eq
ua
tio
n.
12. y =
x +
4
13. y =
-2x -
1
14. x +
y =
-3
x
y
O
x
y
O
x
y
O
15. V
IDEO
REN
TA
LS
A v
ideo
sto
re c
harg
es $
10 f
or a
ren
tal
card
p
lus
$2 p
er r
enta
l.
a.
Wri
te a
n e
qu
ati
on i
n s
lop
e-in
terc
ept
form
for
th
e to
tal
cost
c
of b
uyin
g a
ren
tal
card
an
d r
enti
ng m
mov
ies.
b.
Gra
ph
th
e eq
uati
on.
c.
Fin
d t
he
cost
of
bu
yin
g a
ren
tal
card
an
d 6
mov
ies.
$22
4-1
Vid
eo S
tore
Ren
tal
Co
sts
Total Cost ($)
10 0
12
14
16
18
20c
Movi
es R
ente
d
12
34
5m
c=
10
+2m
c =
10 +
2m
Answers (Lesson 4-1)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
8
Gle
ncoe A
lgeb
ra 1
Practi
ce
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rmW
rit
e a
n e
qu
ati
on
of
a l
ine i
n s
lop
e-i
nte
rcep
t fo
rm
wit
h t
he g
iven
slo
pe a
nd
y-i
nte
rcep
t.
1. sl
ope:
1
−
4 , y-i
nte
rcep
t: 3
y =
1 −
4 x
+ 3
2. sl
ope:
3
−
2 , y-i
nte
rcep
t: -
4 y
= 3
−
2 x
-4
3. sl
ope:
1.5
, y-i
nte
rcep
t: -
1
4. sl
ope:
-2.5
, y-i
nte
rcep
t: 3
.5
y
= 1
.5x -
1
y =
-2.5
x +
3.5
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r e
ach
gra
ph
sh
ow
n.
5.
( –5
, 0
)
( 0,
2)
x
y
O
6.
( –2
, 0
)
( 0,
3)
x
y O
7.
( –3
, 0
)
( 0,
–2)
x
y
O
y =
2 −
5 x
+ 2
y
= 3
−
2 x
+ 3
y
= - 2
−
3 x
- 2
Gra
ph
ea
ch
eq
ua
tio
n.
8. y =
- 1
−
2 x
+ 2
9. 3y =
2x -
6
10. 6x +
3y =
6
x
y
O
x
y
O
x
y
O
11. W
RIT
ING
Carl
a h
as
alr
ead
y w
ritt
en 1
0 p
ages
of
a n
ovel
. S
he
pla
ns
to w
rite
15 a
dd
itio
nal
pages
per
mon
th u
nti
l sh
e is
fin
ish
ed.
a.
Wri
te a
n e
qu
ati
on t
o fi
nd
th
e to
tal
nu
mber
of
pages
P
wri
tten
aft
er a
ny n
um
ber
of
mon
ths m
. P
= 1
0 +
15m
b.
Gra
ph
th
e eq
uati
on o
n t
he
gri
d a
t th
e ri
gh
t.
c.
Fin
d t
he
tota
l n
um
ber
of
pages
wri
tten
aft
er 5
mon
ths.
85
Carla
’s N
ovel
Month
s
Pages Written
20
46
13
5m
P
100
80
60
40
20
4-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-1
Ch
ap
ter
4
9
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
1.SA
VIN
GS
Wad
e’s
gra
nd
mot
her
gave
him
$100 f
or h
is b
irth
day.
Wad
e w
an
ts t
o sa
ve
his
mon
ey t
o bu
y a
new
MP
3 p
layer
th
at
cost
s $275.
Each
mon
th,
he
ad
ds
$25 t
o h
is M
P3 s
avin
gs.
Wri
te a
n
equ
ati
on i
n s
lop
e-in
terc
ept
form
for
m,
the
nu
mber
of
mon
ths
that
it w
ill
tak
e W
ad
e to
save
$275.
2
75 =
25x +
100
2. C
AR
CA
RE
Su
pp
ose
regu
lar
gaso
lin
e co
sts
$2.7
6 p
er g
all
on.
You
can
pu
rch
ase
a c
ar
wash
at
the
gas
stati
on f
or $
3.
Th
e gra
ph
of
the
equ
ati
on f
or t
he
cost
of
gaso
lin
e an
d a
car
wash
is
show
n b
elow
. W
rite
th
e eq
uati
on i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
show
n o
n t
he
gra
ph
.
Gaso
lin
e (
gal)
32
10
54
98
710
y
x6
Cost of gas and car wash ($)
68 4 2
10
16
14
12
18
24
22
20
( 4,
14
.04
)
( 2,
8.5
2)
( 0,
3)
y=
2.7
6x+
3
3. A
DU
LT E
DU
CA
TIO
N A
ngie
’s m
oth
er
wan
ts t
o ta
ke
som
e ad
ult
ed
uca
tion
cl
ass
es a
t th
e lo
cal
hig
h s
choo
l. S
he
has
to p
ay a
on
e-ti
me
enro
llm
ent
fee
of $
25
to j
oin
th
e ad
ult
ed
uca
tion
com
mu
nit
y,
an
d t
hen
$45 f
or e
ach
cla
ss s
he
wan
ts t
o ta
ke.
Th
e eq
uati
on y
= 4
5x +
25
ex
pre
sses
th
e co
st o
f ta
kin
g c
lass
es.
Wh
at
are
th
e sl
ope
an
d y
-in
terc
ept
of
the
equ
ati
on?
m
= 4
5;
y-i
nte
rcep
t =
25
4.B
US
INE
SS
A c
onst
ruct
ion
cre
w n
eed
s to
re
nt
a t
ren
ch d
igger
for
up
to
a w
eek
. A
n
equ
ipm
ent
ren
tal
com
pan
y c
harg
es $
40
per
day p
lus
a $
20 n
on-r
efu
nd
able
in
sura
nce
cos
t to
ren
t a t
ren
ch d
igger
. W
rite
an
d g
rap
h a
n e
qu
ati
on t
o fi
nd
th
e to
tal
cost
to
ren
t th
e tr
ench
dig
ger
for
d
days.
Days
32
10
54
98
76
Price ($)
100
140
60
20
180
300
340
260
220
5. EN
ER
GY
Fro
m 2
002 t
o 2005,
U.S
. co
nsu
mp
tion
of
ren
ewable
en
ergy
incr
ease
d a
n a
ver
age
of 0
.17 q
uad
rill
ion
B
TU
s p
er y
ear.
Abou
t 6.0
7 q
uad
rill
ion
B
TU
s of
ren
ewable
pow
er w
ere
pro
du
ced
in
th
e yea
r 2002.
a.
Wri
te a
n e
qu
ati
on i
n s
lop
e-in
terc
ept
form
to
fin
d t
he
am
oun
t of
ren
ewable
p
ower
P (
qu
ad
rill
ion
BT
Us)
pro
du
ced
in
yea
r y b
etw
een
2002 a
nd
2005.
P =
0.1
7y +
6.0
7
b.
Ap
pro
xim
ate
ly h
ow m
uch
ren
ewable
p
ower
was
pro
du
ced
in
2005?
6.5
8 q
uad
rillio
n B
TU
s
c.
If t
he
sam
e tr
end
con
tin
ues
fro
m 2
006
to 2
010,
how
mu
ch r
enew
able
pow
er
wil
l be
pro
du
ced
in
th
e yea
r 2010?
7.4
3 q
uad
rillio
n B
TU
s
4-1
y =
40d
+ 2
0
Answers (Lesson 4-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
10
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Usin
g E
qu
ati
on
s:
Ideal
Weig
ht
You
can
fin
d y
ou
r id
eal
weig
ht
as
foll
ow
s.
A w
om
an
sh
ou
ld w
eig
h 1
00 p
ou
nd
s fo
r th
e f
irst
5 f
eet
of
heig
ht
an
d
5 a
dd
itio
nal
pou
nd
s fo
r each
in
ch o
ver
5 f
eet
(5 f
eet
= 6
0 i
nch
es)
. A
man
sh
ou
ld w
eig
h 1
06 p
ou
nd
s fo
r th
e f
irst
5 f
eet
of
heig
ht
an
d
6 a
dd
itio
nal
pou
nd
s fo
r each
in
ch o
ver
5 f
eet.
Th
ese
form
ula
s ap
ply
to
peop
le w
ith
norm
al
bon
e s
tru
ctu
res.
To d
ete
rmin
e y
ou
r bon
e s
tru
ctu
re,
wra
p y
ou
r th
um
b a
nd
in
dex f
inger
aro
un
d t
he w
rist
of
you
r oth
er
han
d.
If t
he t
hu
mb a
nd
fin
ger
just
tou
ch,
you
have n
orm
al
bon
e s
tru
ctu
re.
If t
hey o
verl
ap
, you
are
sm
all
-bon
ed
. If
th
ey d
on
’t o
verl
ap
, you
are
larg
e-b
on
ed
. S
mall
-bon
ed
peop
le s
hou
ld d
ecr
ease
th
eir
ca
lcu
late
d i
deal
weig
ht
by 1
0%
. L
arg
e-b
on
ed
peop
le s
hou
ld i
ncr
ease
th
e v
alu
e b
y 1
0%
.
Ca
lcu
late
th
e i
dea
l w
eig
hts
of
these p
eo
ple
.
1. w
om
an
, 5 f
t 4 i
n., n
orm
al-
bon
ed
2. m
an
, 5 f
t 11 i
n., l
arg
e-b
on
ed
1
20 l
b
189.2
lb
3. m
an
, 6 f
t 5 i
n., s
mall
-bon
ed
4. you
, if
you
are
at
least
5 f
t ta
ll
1
87.2
lb
A
nsw
ers
will
vary
.
Fo
r E
xercis
es 5
–9,
use t
he f
oll
ow
ing
in
form
ati
on
.
Su
pp
ose
a n
orm
al-
bon
ed
man
is x i
nch
es
tall
. If
he i
s at
least
5 f
eet
tall
, th
en
x -
60 r
ep
rese
nts
th
e n
um
ber
of
inch
es
this
man
is
over
5 f
eet
tall
. F
or
each
of
these
in
ches,
his
id
eal
weig
ht
is i
ncr
ease
d b
y
6 p
ou
nd
s. T
hu
s, h
is p
rop
er
weig
ht
(y)
is g
iven
by t
he f
orm
ula
y =
6(x
- 6
0)
+ 1
06 o
r y =
6x -
254.
If t
he m
an
is
larg
e-b
on
ed
, th
e
form
ula
beco
mes y =
6x -
254 +
0.1
0(6x -
254).
5. W
rite
th
e f
orm
ula
for
the w
eig
ht
of
a l
arg
e-b
on
ed
man
in
slo
pe-i
nte
rcep
t fo
rm.
6. D
eri
ve t
he f
orm
ula
for
the i
deal
weig
ht
(y)
of
a n
orm
al-
bon
ed
fe
male
wit
h h
eig
ht x i
nch
es.
Wri
te t
he f
orm
ula
in
sl
op
e-i
nte
rcep
t fo
rm.
7. D
eri
ve t
he f
orm
ula
in
slo
pe-i
nte
rcep
t fo
rm f
or
the i
deal
weig
ht
(y)
of
a l
arg
e-b
on
ed
fem
ale
wit
h h
eig
ht x i
nch
es.
8. D
eri
ve t
he f
orm
ula
in
slo
pe-i
nte
rcep
t fo
rm f
or
the i
deal
weig
ht
(y)
of
a s
mall
-bon
ed
male
wit
h h
eig
ht x i
nch
es.
9. F
ind
th
e h
eig
hts
at
wh
ich
norm
al-
bon
ed
male
s an
d l
arg
e-b
on
ed
fe
male
s w
ou
ld w
eig
h t
he s
am
e.
4-1
y =
6.6
x -
279.4
y =
5x -
200
y =
5.5
x -
220
y =
5.4
x -
228.6
68 i
n., o
r 5 f
t 8 i
n.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-2
Ch
ap
ter
4
11
Gle
ncoe A
lgeb
ra 1
Exerc
ises
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
po
int
an
d h
as t
he
giv
en
slo
pe.
1.
( 3,
5)
x
y
O
m=
2
2.
( 0,
0)
x
y
O
m=
–2
3.
( 2,
4)
x
y
O
m=
1 2
y
= 2
x -
1
y =
-2x
y =
1 −
2 x
+ 3
4. (8
, 2);
slo
pe -
3
−
4
5. (-
1,
-3);
slo
pe 5
6. (4
, -
5);
slo
pe -
1
−
2
y
= - 3
−
4 x
+ 8
y
= 5
x +
2
y =
- 1
−
2 x
- 3
7. (-
5,
4);
slo
pe 0
8. (2
, 2);
slo
pe 1
−
2
9. (1
, -
4);
slo
pe -
6
y
= 4
y
= 1
−
2 x
+ 1
y
= -
6x +
2
10. (-
3,
0),
m =
2
11. (0
, 4),
m =
-3
12. (0
, 350),
m =
1
−
5
y
= 2
x +
6
y =
-3
x +
4
y =
1 −
5 x
+ 3
50
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Wri
te a
n E
qu
ati
on
Giv
en
th
e S
lop
e a
nd
a P
oin
t
W
rit
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h (-
4,
2)
wit
h a
slo
pe o
f 3.
Th
e l
ine h
as
slop
e 3
. T
o f
ind
th
e
y-i
nte
rcep
t, r
ep
lace
m w
ith
3 a
nd
(x, y)
wit
h (
-4,
2)
in t
he s
lop
e-i
nte
rcep
t fo
rm.
Th
en
solv
e f
or b
.
y =
mx +
b
Slo
pe-inte
rcept
form
2 =
3(-
4)
+ b
m
= 3
, y =
2,
and x
= -
4
2 =
-12 +
b
Multip
ly.
14 =
b
Add 1
2 t
o e
ach s
ide.
Th
ere
fore
, th
e e
qu
ati
on
is y =
3x +
14.
W
rit
e a
n e
qu
ati
on
of
the l
ine
tha
t p
asses t
hro
ug
h (-
2, -
1)
wit
h a
slo
pe o
f 1
−
4 .
Th
e l
ine h
as
slop
e 1
−
4 .
Rep
lace
m w
ith
1
−
4 a
nd
(x, y)
wit
h (
-2,
-1)
in t
he s
lop
e-i
nte
rcep
t fo
rm.
y =
mx +
b
Slo
pe-inte
rcept
form
-1 =
1
−
4 (
-2)
+ b
m
= 1
−
4 ,
y =
-1,
and x
= -
2
-1 =
- 1
−
2 +
b
Multip
ly.
- 1
−
2 =
b
Add 1
−
2 t
o e
ach s
ide.
Th
ere
fore
, th
e e
qu
ati
on
is y =
1
−
4 x
- 1
−
2 .
4-2
Exam
ple
1Exam
ple
2
Answers (Lesson 4-1 and Lesson 4-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
12
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Wri
te a
n E
qu
ati
on
Giv
en
Tw
o P
oin
ts
W
rit
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h (
1,
2)
an
d (
3,
-2).
F
ind
th
e sl
ope
m.
To
fin
d t
he
y-i
nte
rcep
t, r
epla
ce m
wit
h i
ts c
omp
ute
d v
alu
e an
d (
x,
y)
wit
h
(1,
2)
in t
he
slop
e-in
terc
ept
form
. T
hen
sol
ve
for
b.
m =
y 2 -
y 1 −
x 2 -
x 1
Slo
pe f
orm
ula
m =
-2 -
2 −
3 -
1
y2 =
-2,
y1 =
2,
x2 =
3,
x1 =
1
m =
-2
Sim
plif
y.
y =
mx +
b
Slo
pe-inte
rcept
form
2 =
-2(1
) +
b
Repla
ce m
with -
2,
y w
ith 2
, and x
with 1
.
2 =
-2 +
b
Multip
ly.
4 =
b
Add 2
to e
ach s
ide.
Th
eref
ore,
th
e eq
uati
on i
s y =
-2
x +
4.
Exerc
ises
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
( 1,
1)
( 0,
–3
)
x
y
O
2.
( 0,
4)
( 4,
0)
x
y
O
3.
( 0,
1)
( –3
, 0)
x
y
O
y =
4x -
3
y =
-x +
4
y =
1
−
3 x
+ 1
4. (-
1,
6),
(7, -
10)
5. (0
, 2),
(1,
7)
6. (6
, -
25),
(-
1,
3)
y =
-2x +
4
y =
5x +
2
y =
-4x -
1
7. (-
2, -
1),
(2,
11)
8. (1
0, -
1),
(4,
2)
9. (-
14, -
2),
(7,
7)
y =
3x +
5
y =
- 1
−
2 x
+ 4
y =
3
−
7 x
+ 4
10. (4
, 0),
(0,
2)
11. (-
3,
0),
(0,
5)
12. (0
, 16),
(-
10,
0)
y =
- 1
−
2 x
+ 2
y =
5
−
3 x
+ 5
y =
8
−
5 x
+ 1
6
4-2 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-2
Ch
ap
ter
4
13
Gle
ncoe A
lgeb
ra 1
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
po
int
wit
h t
he
giv
en
slo
pe.
1.
( –1
, 4
)
x
y
O
m=
–3
2.
( 4,
1)
x
y
O
m=
1
3.
( -1
, 2
)
x
y O
m=
2
y =
-3x +
1
y =
x -
3
y =
2x +
4
4. (1
, 9);
slo
pe
4
5. (4
, 2);
slo
pe -
2
6. (2
, -
2);
slo
pe
3
y =
4x +
5
y =
-2
x +
10
y =
3x -
8
7. (3
, 0);
slo
pe
5
8. (-
3, -
2);
slo
pe
2
9. (-
5,
4);
slo
pe -
4
y =
5x -
15
y =
2x +
4
y =
-4
x -
16
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
10.
( –2
, 3
)
( 3,
–2
)
x
y
O
11.
( –1
, –
3)
( 1,
1)
x
y
O
12.
( 2,
–1)
( 0,
3)
x
y
O
y =
-x +
1
y =
2x -
1
y =
-2x +
3
13. (1
, 3),
(-
3, -
5)
14. (1
, 4),
(6, -
1)
15. (1
, -
1),
(3,
5)
y =
2x +
1
y =
-x +
5
y =
3x -
4
16. (-
2,
4),
(0,
6)
17. (3
, 3),
(1, -
3)
18. (-
1,
6),
(3, -
2)
y =
x +
6
y =
3x -
6
y =
-2
x +
4
19. IN
VESTIN
G T
he
pri
ce o
f a s
hare
of
stoc
k i
n X
YZ
Cor
por
ati
on w
as
$74 t
wo
wee
ks
ago.
S
even
wee
ks
ago,
th
e p
rice
was
$59 a
sh
are
.
a.
Wri
te a
lin
ear
equ
ati
on t
o fi
nd
th
e p
rice
p o
f a s
hare
of
XY
Z C
orp
orati
on s
tock
w
wee
ks
from
now
.
p =
3w
+ 8
0
b.
Est
imate
th
e p
rice
of
a s
hare
of
stoc
k f
ive
wee
ks
ago.
$65
Sk
ills
Pra
ctic
e
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
4-2
Answers (Lesson 4-2)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
14
Gle
ncoe A
lgeb
ra 1
Practi
ce
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
po
int
an
d h
as t
he
giv
en
slo
pe.
1.
( 1,
2)
x
y
O
m=
3
2.
( –2
, 2
)
x
y O
m=
–2
3.
( –1
, –
3)
x
y
O
m=
–1
y
= 3
x -
1
y =
-2x -
2
y =
-x -
4
4. (-
5,
4);
slo
pe -
3
5. (4
, 3);
slo
pe
1 −
2
6. (1
, -
5);
slo
pe - 3
−
2
y
= -
3x -
11
y =
1 −
2 x
+ 1
y
= - 3
−
2 x
- 7
−
2
7. (3
, 7);
slo
pe
2 −
7
8. (-
2,
5 −
2 ) ;
slop
e - 1
−
2
9. (5
, 0);
slo
pe
0
y
= 2
−
7 x
+ 6
1 −
7
y =
- 1
−
2 x
+ 3
−
2
y =
0
Writ
e a
n e
qu
ati
on
of
the l
ine t
ha
t p
asses t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
10.
( 4,
–2
)
( 2,
–4
)
x
y
O
11.
( 0,
5)
( 4,
1) x
y
O
12.
( –3
, 1
)
( –1
, –
3)
x
y
O
y
= x
- 6
y
= -
x +
5
y =
-2x -
5
13. (0
, -
4),
(5, -
4)
14. (-
4, -
2),
(4,
0)
15. (-
2, -
3),
(4,
5)
y
= -
4
y =
1 −
4 x
- 1
y
= 4
−
3 x
- 1
−
3
16. (0
, 1),
(5,
3)
17. (-
3,
0),
(1, -
6)
18. (1
, 0),
(5, -
1)
y
= 2
−
5 x
+ 1
y
= - 3
−
2 x
- 9
−
2
y =
- 1
−
4 x
+ 1
−
4
19. D
AN
CE L
ESSO
NS
Th
e co
st f
or 7
dan
ce l
esso
ns
is $
82.
Th
e co
st f
or 1
1 l
esso
ns
is $
122.
Wri
te a
lin
ear
equ
ati
on t
o fi
nd
th
e to
tal
cost
C f
or ℓ
les
son
s. T
hen
use
th
e eq
uati
on t
o fi
nd
th
e co
st o
f 4 l
esso
ns.
20. W
EA
TH
ER
It
is 7
6°F
at
the
6000-f
oot
level
of
a m
oun
tain
, an
d 4
9°F
at
the
12,0
00-f
oot
level
of
the
mou
nta
in.
Wri
te a
lin
ear
equ
ati
on t
o fi
nd
th
e te
mp
eratu
re T
at
an
ele
vati
on
x o
n t
he
mou
nta
in,
wh
ere x i
s in
th
ousa
nd
s of
fee
t.
4-2
C =
10ℓ +
12;
$52
T =
-4.5
x +
103
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-2
Ch
ap
ter
4
15
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
1.FU
ND
RA
ISIN
G Y
von
ne
an
d h
er f
rien
ds
hel
d a
bak
e sa
le t
o ben
efit
a s
hel
ter
for
hom
eles
s p
eop
le.
Th
e fr
ien
ds
sold
22
cak
es o
n t
he
firs
t d
ay a
nd
15 c
ak
es o
n
the
seco
nd
day o
f th
e bak
e sa
le.
Th
ey
coll
ecte
d $
88 o
n t
he
firs
t d
ay a
nd
$60 o
n
the
seco
nd
day.
Let
x r
epre
sen
t th
e n
um
ber
of
cak
es s
old
an
d y
rep
rese
nt
the
am
oun
t of
mon
ey m
ad
e. F
ind
th
e sl
ope
of
the
lin
e th
at
wou
ld p
ass
th
rou
gh
th
e
poi
nts
giv
en.
4
2. JO
BS
Mr.
Kim
ball
rec
eives
a $
3000
an
nu
al
sala
ry i
ncr
ease
on
th
e an
niv
ersa
ry o
f h
is h
irin
g i
f h
e re
ceiv
es
a s
ati
sfact
ory p
erfo
rman
ce r
evie
w.
His
sta
rtin
g s
ala
ry w
as
$41,2
50.
Wri
te
an
equ
ati
on t
o sh
ow k
, M
r. K
imball
’s
sala
ry a
fter
y y
ears
at
this
com
pan
y
if h
is p
erfo
rman
ce r
evie
ws
are
alw
ays
sati
sfact
ory.
k
= 3
000y +
41,2
50
3.C
EN
SU
S T
he
pop
ula
tion
of
Lare
do,
T
exas,
was
abou
t 215,5
00 i
n 2
007.
It
was
abou
t 123,0
00 i
n 1
990.
If w
e ass
um
e th
at
the
pop
ula
tion
gro
wth
is
con
stan
t an
d y
rep
rese
nts
th
e n
um
ber
of
yea
rs
aft
er 1
990,
wri
te a
lin
ear
equ
ati
on t
o fi
nd
p,
Lare
do’
s p
opu
lati
on f
or a
ny y
ear
aft
er 1
990.
p
= 5
441y +
123,0
00
4.W
ATER
Mr.
Wil
liam
s p
ays
$40 a
mon
th
for
city
wate
r, n
o m
att
er h
ow m
an
y
gall
ons
of w
ate
r h
e u
ses
in a
giv
en
mon
th.
Let
x r
epre
sen
t th
e n
um
ber
of
gall
ons
of w
ate
r u
sed
per
mon
th.
Let
yre
pre
sen
t th
e m
onth
ly c
ost
of t
he
city
w
ate
r in
dol
lars
. W
hat
is t
he
equ
ati
on o
f th
e li
ne
that
rep
rese
nts
th
is i
nfo
rmati
on?
Wh
at
is t
he
slop
e of
th
e li
ne?
y
= 4
0;
slo
pe i
s 0
. T
he l
ine i
s
ho
rizo
nta
l.
5. SH
OE S
IZES
Th
e ta
ble
sh
ows
how
w
omen
’s s
hoe
siz
es i
n t
he
Un
ited
K
ingd
om c
omp
are
to
wom
en’s
sh
oe s
izes
in
th
e U
nit
ed S
tate
s.
Wo
men
’s S
ho
e S
izes
U.K
.3
3.5
44.5
55.5
6
U.S
.5.5
66
.57
7.5
88.5
So
urce:
Dance
Sport
UK
a.
Wri
te a
lin
ear
equ
ati
on t
o d
eter
min
e an
y U
.S.
size
if
you
are
giv
en t
he
U.K
. si
ze.
y =
x +
2.5
b.
Wh
at
is t
he
slop
e an
d y
-in
terc
ept
of
the
lin
e?
S
lop
e =
1;
y-i
nte
rcep
t =
2.5
c.
Is t
he y-i
nte
rcep
t a v
ali
d d
ata
poi
nt
for
the
giv
en i
nfo
rmati
on?
No
. It
is n
ot
likely
a v
alid
data
p
oin
t b
ecau
se t
he U
.K.
siz
ing
p
rob
ab
ly d
oes n
ot
inclu
de
zero
. H
ow
ever,
th
e p
oin
t is
th
e y
-in
terc
ep
t o
f th
e l
ine
rep
resen
ted
by t
he d
ata
if
the d
ata
were
to
co
nti
nu
e
ind
efi
nit
ely
in
bo
th d
irecti
on
s.
4-2
Answers (Lesson 4-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
16
Gle
ncoe A
lgeb
ra 1
Tan
gen
t to
a C
urv
eA
tan
gen
t li
ne i
s a l
ine t
hat
inte
rsect
s a c
urv
e a
t a p
oin
t w
ith
th
e s
am
e r
ate
of
chan
ge,
or
slop
e,
as
the r
ate
of
chan
ge o
f th
e c
urv
e a
t th
at
poin
t.
For
qu
ad
rati
c fu
nct
ion
s (f
un
ctio
ns
of
the f
orm
ax
2 +
bx
+ c
), t
he e
qu
ati
on
of
the t
an
gen
t li
ne
can
be f
ou
nd
. T
his
is
base
d o
n t
he f
act
th
at
the s
lop
e t
hro
ugh
an
y t
wo p
oin
ts o
n t
he c
urv
e
is e
qu
al
to t
he s
lop
e o
f th
e l
ine t
an
gen
t to
th
e c
urv
e a
t th
e p
oin
t w
hose
x-v
alu
e i
s h
alf
way
betw
een
th
e x
-valu
es
of
the o
ther
two p
oin
ts.
T
o f
ind
th
e e
qu
ati
on
of
a t
an
gen
t li
ne t
o t
he c
urv
e y
= x
2 +
3x +
2 t
hro
ug
h t
he
po
int
(2,
12),
fir
st
fin
d t
wo
po
ints
on
th
e c
urv
e
wh
ose x
-va
lues a
re e
qu
idis
tan
t fr
om
th
e x
-va
lue
of
the p
oin
t th
e t
an
gen
t n
eed
s t
o g
o t
hro
ug
h.
Ste
p 1
: F
ind
tw
o m
ore
poin
ts.
Use
x =
1 a
nd
x =
3.
W
hen
x =
1,
y =
12 +
3(1
) +
2 o
r 6.
W
hen
x =
3,
y =
32 +
3(3
) +
2 o
r 20.
S
o,
the t
wo o
rdere
d p
air
s are
(1,
6)
an
d (
3,
20).
Ste
p 2
: F
ind
th
e s
lop
e o
f th
e l
ine t
hat
goes
thro
ugh
th
ese
tw
o p
oin
ts.
m =
20 -
6
−
3 -
1
or
7
Ste
p 3
: N
ow
use
th
is s
lop
e a
nd
th
e p
oin
t (2
, 12)
to f
ind
th
e e
qu
ati
on
of
the t
an
gen
t li
ne.
y =
mx +
b
Slo
pe "
inte
rcept
form
.
1
2 =
7(2
) +
b
Repla
ce x
with 2
, y w
ith 1
2,
and m
with 7
.
-2 =
b
S
olv
e f
or
b.
So,
the e
qu
ati
on
of
the t
an
gen
t li
ne t
o y
= x
2 +
3x
+ 2
th
rou
gh
th
e p
oin
t (2
, 12)
is y
= 7
x –
2.
Exerc
ises
Fo
r 1
–3,
fin
d t
he e
qu
ati
on
s o
f th
e l
ines t
an
gen
t to
ea
ch
cu
rv
e t
hro
ug
h t
he
giv
en
po
int.
1. y =
x2 -
3x +
7,
(2,
5)
2. y =
3x
2 +
4x -
5,
(-4,
27)
3. y =
5 -
x2,
(1,
4)
y
= x
+ 3
y
= -
20x -
53
y
= -
2x +
6
4. F
ind
th
e s
lop
e o
f th
e l
ine t
an
gen
t to
th
e c
urv
e a
t x =
0 f
or
the g
en
era
l equ
ati
on
y =
ax
2 +
bx +
c.
m
= b
5. F
ind
th
e s
lop
e o
f th
e l
ine t
an
gen
t to
th
e c
urv
e y
= a
x2 +
bx +
c a
t x b
y f
ind
ing t
he s
lop
e
of
the l
ine t
hro
ugh
th
e p
oin
ts (
0,
c) a
nd
(2
x,
4a
x2 +
2bx +
c).
Does
this
an
swer
work
for
x =
0 i
n t
he a
nsw
er
you
fou
nd
to p
roble
m 4
? m
= 2
ax +
b,
yes
En
rich
men
t
y
xO
4-2 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-3
Ch
ap
ter
4
17
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Po
int-
Slo
pe F
orm
Po
int-
Slo
pe F
orm
Po
int-
Slo
pe F
orm
y -
y1 =
m(x
- x
1),
where
(x
1,
y1)
is a
giv
en p
oin
t on a
nonvert
ical lin
e
and m
is t
he s
lope o
f th
e lin
e
W
rit
e a
n e
qu
ati
on
in
p
oin
t-slo
pe f
orm
fo
r t
he l
ine t
ha
t p
asses
thro
ug
h (
6,
1)
wit
h a
slo
pe o
f -
5
−
2 .
y -
y1 =
m(x
- x
1)
Poin
t-slo
pe f
orm
y -
1 =
- 5
−
2 (x -
6)
m =
- 5
−
2 ;
(x1,
y1)
= (
6,
1)
Th
ere
fore
, th
e e
qu
ati
on
is
y -
1 =
- 5
−
2 (x
- 6
).
W
rit
e a
n e
qu
ati
on
in
p
oin
t-slo
pe f
orm
fo
r a
ho
riz
on
tal
lin
e
tha
t p
asses t
hro
ug
h (
4,
-1).
y -
y1 =
m(x
- x
1)
Poin
t-slo
pe f
orm
y -
(-
1)
= 0
(x -
4)
m =
0;
(x1,
y1)
= (
4,
-1)
y +
1 =
0
Sim
plif
y.
Th
ere
fore
, th
e e
qu
ati
on
is
y +
1 =
0.
Exerc
ises
Writ
e a
n e
qu
ati
on
in
po
int-
slo
pe f
orm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
p
oin
t w
ith
th
e s
lop
e p
ro
vid
ed
.
1.
( 4,
1)
x
y
O
m=
1
2.
( –3
, 2)
x
y
O
m=
0
3.
( 2,
–3
)x
y
O
m=
–2
y
- 1
= x
- 4
y
- 2
= 0
y
+ 3
= -
2(x
- 2
)
4. (2
, 1),
m =
4
5. (-
7,
2),
m =
6
6. (8
, 3),
m =
1
y
- 1
= 4
(x -
2)
y -
2 =
6(x
+ 7
) y
- 3
= x
- 8
7. (-
6,
7),
m =
0
8. (4
, 9),
m =
3
−
4
9. (-
4,
-5),
m =
- 1
−
2
y
- 7
= 0
y
- 9
= 3
−
4 (x -
4)
y +
5 =
- 1
−
2 (x +
4)
10. W
rite
an
equ
ati
on
in
poin
t-sl
op
e f
orm
for
a h
ori
zon
tal
lin
e t
hat
pass
es
thro
ugh
(4
, -
2).
11. W
rite
an
equ
ati
on
in
poin
t-sl
op
e f
orm
for
a h
ori
zon
tal
lin
e t
hat
pass
es
thro
ugh
(-
5,
6).
12. W
rite
an
equ
ati
on
in
poin
t-sl
op
e f
orm
for
a h
ori
zon
tal
lin
e t
hat
pass
es
thro
ugh
(5,
0).
y
= 0
4-3
Exam
ple
1Exam
ple
2
y +
2 =
0
y -
6 =
0
Answers (Lesson 4-2 and Lesson 4-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
18
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Po
int-
Slo
pe F
orm
Fo
rms
of
Lin
ear
Eq
uati
on
s
Slo
pe-I
nte
rcep
t
Fo
rmy =
mx +
bm
= s
lope;
b =
y-inte
rcept
Po
int-
Slo
pe
Fo
rmy -
y1 =
m(x
- x
1)
m =
slo
pe;
(x1,
y1)
is a
giv
en p
oin
t.
Sta
nd
ard
Fo
rmA
x +
By =
CA
and B
are
not
both
zero
. U
sually
A is n
onnegative a
nd A
, B
, and
C a
re inte
gers
whose g
reate
st
com
mon f
acto
r is
1.
W
rit
e y
+ 5
= 2
−
3 (x
- 6
) in
sta
nd
ard
fo
rm
.
y +
5 =
2 −
3 (x -
6)
Origin
al equation
3(y
+ 5
) =
3 ( 2
−
3 ) (x
- 6
) M
ultip
ly e
ach s
ide b
y 3
.
3y +
15 =
2(x
- 6
) D
istr
ibutive P
ropert
y
3y +
15 =
2x -
12
Dis
trib
utive P
ropert
y
3
y =
2x -
27
S
ubtr
act
15 f
rom
each s
ide.
-2
x +
3y =
-27
Add -
2x t
o e
ach s
ide.
2
x -
3y =
27
M
ultip
ly e
ach s
ide b
y -
1.
Th
ere
fore
, th
e s
tan
dard
form
of
the e
qu
ati
on
is
2x -
3y =
27
.
W
rit
e y
- 2
= -
1 −
4 (x -
8)
in
slo
pe-i
nte
rcep
t fo
rm
.
y -
2 =
- 1
−
4 (x
- 8
) O
rigin
al equation
y -
2 =
- 1
−
4 x
+ 2
D
istr
ibutive P
ropert
y
y =
- 1
−
4 x
+ 4
A
dd 2
to e
ach s
ide.
Th
ere
fore
, th
e s
lop
e-i
nte
rcep
t fo
rm o
f th
e
equ
ati
on
is
y =
- 1
−
4 x
+ 4
.
Exerc
ises
Writ
e e
ach
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
1. y +
2 =
-3(x
- 1
) 2. y -
1 =
- 1
−
3 (x -
6)
3. y +
2 =
2 −
3 (x -
9)
3
x +
y =
1
x +
3y =
9
2x -
3y =
24
4. y +
3 =
-(x
- 5
) 5. y -
4 =
5 −
3 (x +
3)
6. y +
4 =
- 2
−
5 (x -
1)
x
+ y
= 2
5
x -
3y =
-27
2x +
5y =
-18
Writ
e e
ach
eq
ua
tio
n i
n s
lop
e-i
nte
rcep
t fo
rm
.
7. y +
4 =
4(x
- 2
) 8. y -
5 =
1 −
3 (x -
6)
9. y
- 8
= - 1
−
4 (x
+ 8
)
y
= 4
x -
12
y
= 1
−
3 x
+ 3
y
= - 1
−
4 x
+ 6
10. y -
6 =
3 (x -
1 −
3 )
11. y +
4 =
-2(x
+ 5
) 12. y +
5 −
3 =
1 −
2 (x
- 2
)
y
= 3
x +
5
y =
-2
x -
14
y
= 1
−
2 x
- 8
−
3
4-3
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-3
Ch
ap
ter
4
19
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Po
int-
Slo
pe F
orm
Writ
e a
n e
qu
ati
on
in
po
int-
slo
pe f
orm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
p
oin
t w
ith
th
e s
lop
e p
ro
vid
ed
.
1.
( –1
, –
2)
x
y
O
m=
3
2.
( 1,
–2
)x
y O
m=
–1
3.
( 2,
–3)
x
y O
m=
0
y
+ 2
= 3
(x +
1)
y +
2 =
-(x
- 1
) y
+ 3
= 0
4. (3
, 1),
m =
0
5. (-
4,
6),
m =
8
6. (1
, -
3),
m =
-4
y
- 1
= 0
y
- 6
= 8
(x +
4)
y +
3 =
-4(x
- 1
)
7. (4
, -
6),
m =
1
8. (3
, 3),
m =
4 −
3
9. (-
5, -
1),
m =
- 5
−
4
y
+ 6
= x
- 4
y
- 3
= 4
−
3 (x -
3)
y +
1 =
- 5
−
4 (x +
5)
Writ
e e
ach
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
10. y +
1 =
x +
2
11. y +
9 =
-3(x
- 2
) 12. y -
7 =
4(x
+ 4
)
x
- y
= -
1
3x +
y =
-3
4x -
y =
-23
13. y -
4 =
-(x
- 1
) 14. y -
6 =
4(x
+ 3
) 15. y +
5 =
-5(x
- 3
)
x
+ y
= 5
4
x -
y =
-18
5x +
y =
10
16. y -
10 =
-2(x
- 3
) 17. y -
2 =
- 1
−
2 (x
- 4
) 18. y +
11 =
1 −
3 (x +
3)
2
x +
y =
16
x +
2y =
8
x -
3y =
30
Writ
e e
ach
eq
ua
tio
n i
n s
lop
e-i
nte
rcep
t fo
rm
.
19. y -
4 =
3(x
- 2
) 20. y +
2 =
-(x
+ 4
) 21. y -
6 =
-2(x
+ 2
)
y
= 3
x -
2
y =
-x -
6
y =
-2
x +
2
22. y +
1 =
-5(x
- 3
) 23. y -
3 =
6(x
- 1
) 24. y -
8 =
3(x
+ 5
)
y
= -
5x +
14
y =
6x -
3
y =
3x +
23
25. y -
2 =
1 −
2 (x
+ 6
) 26. y +
1 =
- 1
−
3 (x
+ 9
) 27. y -
1 −
2 =
x +
1 −
2
y
= 1
−
2 x
+ 5
y
= - 1
−
3 x
- 4
y
= x
+ 1
4-3
Answers (Lesson 4-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
20
Gle
ncoe A
lgeb
ra 1
Practi
ce
Po
int-
Slo
pe F
orm
Writ
e a
n e
qu
ati
on
in
po
int-
slo
pe f
orm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he g
iven
po
int
wit
h t
he s
lop
e p
ro
vid
ed
.
1. (2
, 2),
m =
-3
2. (1
, -
6),
m =
-1
3. (-
3,
-4),
m =
0
y
- 2
= -
3(x
- 2
) y
+ 6
= -
(x -
1)
y +
4 =
0
4. (1
, 3),
m =
- 3
−
4
5. (-
8,
5),
m =
- 2
−
5
6. (3
, -
3),
m =
1
−
3
y
- 3
= -
3
−
4 (x -
1)
y -
5 =
- 2
−
5 (x +
8)
y +
3 =
1
−
3 (x -
3)
Writ
e e
ach
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
7. y -
11 =
3(x
- 2
) 8. y -
10
= -
(x -
2)
9. y +
7 =
2(x
+ 5
)
3
x -
y =
-5
x +
y =
12
2
x -
y =
-3
10. y -
5 =
3
−
2 (x
+ 4
) 11. y +
2 =
- 3
−
4 (x
+ 1
) 12. y -
6 =
4
−
3 (x
- 3
)
3
x -
2y =
-22
3x +
4y =
-11
4x -
3y =
-6
13. y +
4 =
1.5
(x +
2)
14. y -
3 =
-2.4
(x -
5)
15. y -
4 =
2.5
(x +
3)
3
x -
2y =
2
12
x +
5y =
75
5
x -
2y =
-23
Writ
e e
ach
eq
ua
tio
n i
n s
lop
e-i
nte
rcep
t fo
rm
.
16. y +
2 =
4(x
+ 2
) 17. y +
1 =
-7(x
+ 1
) 18. y -
3 =
-5(x
+ 1
2)
y
= 4
x +
6
y =
-7
x -
8
y =
-5
x -
57
19. y -
5 =
3
−
2 (x
+ 4
) 20. y -
1
−
4 =
- 3
(x +
1
−
4 )
21. y -
2
−
3 =
-2 (x
- 1
−
4 )
y
= 3
−
2 x
+ 1
1
y =
-3
x -
1
−
2
y =
-2
x +
7
−
6
22. C
ON
STR
UC
TIO
N A
con
stru
ctio
n c
omp
an
y c
harg
es $
15 p
er h
our
for
deb
ris
rem
oval,
p
lus
a o
ne-
tim
e fe
e fo
r th
e u
se o
f a t
rash
du
mp
ster
. T
he
tota
l fe
e fo
r 9 h
ours
of
serv
ice
is $
195.
a.
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
equ
ati
on t
o fi
nd
th
e to
tal
fee y f
or a
ny n
um
ber
of
hou
rs x
.
b.
Wri
te t
he
equ
ati
on i
n s
lop
e-in
terc
ept
form
. y =
15
x +
60
c.
Wh
at
is t
he
fee
for
the
use
of
a t
rash
du
mp
ster
? $60
23. M
OV
ING
Th
ere
is a
set
dail
y f
ee f
or r
enti
ng a
mov
ing t
ruck
, p
lus
a c
harg
e of
$0.5
0 p
er
mil
e d
riven
. It
cos
ts $
64 t
o re
nt
the
tru
ck o
n a
day w
hen
it
is d
riven
48 m
iles
.
a.
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
equ
ati
on t
o fi
nd
th
e to
tal
charg
e y f
or a
ny n
um
ber
of
mil
es x
for
a o
ne-
day r
enta
l.
b.
Wri
te t
he
equ
ati
on i
n s
lop
e-in
terc
ept
form
.
c.
Wh
at
is t
he
dail
y f
ee?
$40
4-3
y -
195 =
15
(x -
9)
y -
64
= 0
.5(x
- 4
8)
y =
0.5
x +
40
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-3
Ch
ap
ter
4
21
Gle
ncoe A
lgeb
ra 1
1.B
ICY
CLIN
G H
arv
ey r
ides
his
bik
e at
an
aver
age
spee
d o
f 12 m
iles
per
hou
r. I
n
oth
er w
ord
s, h
e ri
des
12 m
iles
in
1 h
our,
24 m
iles
in
2 h
ours
, an
d s
o on
. L
et h
be
the
nu
mber
of
hou
rs h
e ri
des
an
d d
be
dis
tan
ce t
ravel
ed.
Wri
te t
he
equ
ati
on f
or
the
rela
tion
ship
bet
wee
n d
ista
nce
an
d
tim
e in
poi
nt-
slop
e fo
rm.
d
- 1
2 =
12(h
- 1
)
2. G
EO
METR
Y T
he
per
imet
er o
f a s
qu
are
vari
es d
irec
tly w
ith
th
e si
de
len
gth
. T
he
poi
nt-
slop
e fo
rm o
f th
e eq
uati
on f
or t
his
fu
nct
ion
is y -
4 =
4(x
- 1
). W
rite
th
e eq
uati
on i
n s
tan
dard
for
m.
4
x -
y =
0
3.N
ATU
RE
In
a n
ear
per
fect
lin
ear
rela
tion
ship
, th
e fr
equ
ency
of
a m
ale
cr
ick
et’s
ch
irp
matc
hes
th
e ou
tdoo
r te
mp
eratu
re.
Th
e re
lati
onsh
ip i
s ex
pre
ssed
by t
he
equ
ati
on T
= n
+ 4
0,
wh
ere T
is
the
tem
per
atu
re i
n d
egre
es
Fah
ren
hei
t an
d n
is
the
nu
mber
of
chir
ps
the
cric
ket
mak
es i
n 1
4 s
econ
ds.
Use
th
e in
form
ati
on o
n t
he
gra
ph
bel
ow t
o w
rite
a p
oin
t-sl
ope
form
of
the
equ
ati
on
for
the
lin
e.
Nu
mb
er
of
Ch
irp
s
15
10
50
25
20
y
x30
35
Temperature (°F)
30
40
20
10
50
70
60
S
am
ple
an
sw
er:
T
- 6
0 =
1(n
- 2
0)
4.C
AN
OEIN
G G
eoff
pad
dle
s h
is c
an
oe a
t an
aver
age
spee
d o
f 3.5
mil
es p
er h
our.
A
fter
5 h
ours
of
can
oein
g,
Geo
ff h
as
travel
ed 1
8 m
iles
. W
rite
an
equ
ati
on i
n
the
poi
nt-
slop
e fo
rm t
o fi
nd
th
e to
tal
dis
tan
ce y
for
an
y n
um
ber
of
hou
rs x
.
y
- 1
8 =
3.5
(x -
5)
5. A
VIA
TIO
N A
jet
pla
ne
tak
es o
ff a
nd
cl
imbs
con
sist
entl
y 2
0 f
eet
for
ever
y 4
0
feet
it
mov
es h
oriz
onta
lly.
Th
e gra
ph
sh
ows
the
traje
ctor
y o
f th
e je
t.
Ho
rizo
nta
l D
ista
nce
(ft
)
500
0
0
1000
1500
2000
2500
Height (ft)
600
800
400
200
1000
1400
1200
a.
Wri
te a
n e
qu
ati
on i
n p
oin
t-sl
ope
form
fo
r th
e li
ne
rep
rese
nti
ng t
he
jet’
s h
oriz
onta
l tr
aje
ctor
y.
y -
0 =
0.5
(x -
0)
b.
Wri
te t
he
equ
ati
on f
rom
part
a i
n
slop
e -i
nte
rcep
t fo
rm.
c.
Wri
te t
he
equ
ati
on i
n s
tan
dard
for
m.
x -
2y =
0
Wo
rd
Pro
ble
m P
racti
ce
Po
int-
Slo
pe F
orm
4-3
y =
0.5
x
Answers (Lesson 4-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
22
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
x
y O
x
y
O
4-3
Co
llin
eari
ty
You
have l
earn
ed
how
to f
ind
th
e s
lop
e b
etw
een
tw
o p
oin
ts o
n a
lin
e.
Does
it m
att
er
wh
ich
tw
o p
oin
ts y
ou
use
? H
ow
does
you
r ch
oic
e o
f p
oin
ts a
ffect
th
e s
lop
e-i
nte
rcep
t fo
rm o
f th
e e
qu
ati
on
of
the l
ine?
1. C
hoose
th
ree d
iffe
ren
t p
air
s of
poin
ts f
rom
th
e g
rap
h a
t th
e
righ
t. W
rite
th
e s
lop
e-i
nte
rcep
t fo
rm o
f th
e l
ine u
sin
g e
ach
pair
.
y
= x
+ 1
2. H
ow
are
th
e e
qu
ati
on
s re
late
d?
T
hey a
re t
he s
am
e.
3. W
hat
con
clu
sion
can
you
dra
w f
rom
you
r an
swers
to E
xerc
ises
1 a
nd
2?
T
he e
qu
ati
on
of
a l
ine i
s t
he s
am
e n
o m
att
er
wh
ich
tw
o p
oin
ts
yo
u c
ho
ose.
Wh
en
poin
ts a
re c
on
tain
ed
in
th
e s
am
e l
ine,
they a
re s
aid
to b
e c
oll
inea
r.
Even
th
ou
gh
poin
ts m
ay look l
ike t
hey f
orm
a s
traig
ht
lin
e w
hen
con
nect
ed
, it
does
not
mean
th
at
they a
ctu
all
y d
o.
By c
heck
ing p
air
s of
poin
ts o
n a
li
ne y
ou
can
dete
rmin
e w
heth
er
the l
ine r
ep
rese
nts
a l
inear
rela
tion
ship
.
4. C
hoose
severa
l p
air
s of
poin
ts f
rom
th
e g
rap
h a
t th
e r
igh
t an
d w
rite
th
e s
lop
e-i
nte
rcep
t fo
rm o
f th
e l
ine u
sin
g e
ach
pair
.
y
= x
; y =
2x -
2;
y =
2x +
1
5. W
hat
con
clu
sion
can
you
dra
w f
rom
you
r equ
ati
on
s in
E
xerc
ise 4
? Is
th
is a
str
aig
ht
lin
e?
T
he p
oin
ts a
re n
ot
co
llin
ear.
Th
is i
s n
ot
a
str
aig
ht
lin
e.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-3
Ch
ap
ter
4
23
Gle
ncoe A
lgeb
ra 1
Gra
ph
ing C
alc
ula
tor
Act
ivit
y
Wri
tin
g L
inear
Eq
uati
on
s
Lis
ts c
an
be u
sed
wit
h t
he l
inear
regre
ssio
n f
un
ctio
n t
o w
rite
an
d v
eri
fy
lin
ear
equ
ati
on
s giv
en
tw
o p
oin
ts o
n a
lin
e,
or
the s
lop
e o
f a l
ine a
nd
a p
oin
t
thro
ugh
wh
ich
it
pass
es.
Th
e l
inear
regre
ssio
n f
un
ctio
n,
Lin
Reg
(ax
+ b
), i
s
fou
nd
un
der
the S
TA
T C
AL
C m
en
u.
W
rit
e t
he s
lop
e-i
nte
rcep
t fo
rm
of
an
eq
ua
tio
n o
f th
e
lin
e t
ha
t p
asses t
hro
ug
h (
3, -
2)
an
d (
6,
4).
En
ter
the x
-coord
inate
s of
the p
oin
ts i
nto
L1
an
d t
he y
-coord
inate
s
into
L2
. U
se t
he l
inear
regre
ssio
n f
un
ctio
n t
o w
rite
th
e e
qu
ati
on
of
the l
ine.
Keyst
rok
es:
S
TA
T
EN
TE
R 3
E
NT
ER
6
EN
TE
R
(–
) 2
E
NT
ER
4
EN
TE
R
ST
AT
4
2nd
[L
1]
,
2nd
[L
2]
EN
TE
R.
Th
e e
qu
ati
on
is y
= 2x
- 8
. If
you
have a
lread
y w
ritt
en
th
e e
qu
ati
on
of
a l
ine,
you
can
use
the g
iven
in
form
ati
on
to v
eri
fy y
ou
r equ
ati
on
.
Exerc
ises
Writ
e t
he s
lop
e-i
nte
rcep
t fo
rm
an
d t
he s
tan
da
rd
fo
rm
of
an
eq
ua
tio
n o
f th
e l
ine
tha
t sa
tisfi
es e
ach
co
nd
itio
n.
1. p
ass
es
thro
ugh
(0,
7)
an
d ( 1
−
7 ,
-5
) 2.
pass
es
thro
ugh
(-
5,
1),
(10,
10),
an
d (
-10,
-2)
y =
-84
x +
7;
84
x +
y =
7
y =
3 −
5 x
+ 4
; 3x -
5y =
- 2
0
3. p
ass
es
thro
ugh
(6,
-4),
m =
2
−
3
4.
pass
es
thro
ugh
(3,
5),
m =
-4
y =
2 −
3 x
- 8
; 2x -
3y =
24
y =
-4x +
17;
4x +
y =
17
5. x-i
nte
rcep
t: 1
, y-i
nte
rcep
t: -
1
−
2
6.
pass
es
thro
ugh
(-
18,
11),
y-i
nte
rcep
t: 3
y =
1 −
2 x
- 1
−
2 ;
x -
2y =
1
y =
- 4
−
9 x
+ 3
; 4x +
9y =
27
V
erif
y t
he e
qu
ati
on
of
a l
ine p
assin
g t
hro
ug
h (
2, -
3)
wit
h s
lop
e - 3
−
4 c
an
be w
rit
ten
as 3x +
4y =
-6.
Use
th
e g
iven
poin
t an
d s
lop
e t
o d
ete
rmin
e a
seco
nd
poin
t th
rou
gh
wh
ich
th
e l
ine p
ass
es.
En
ter
the x
-coord
inate
s of
the p
oin
ts i
nto
L1
an
d t
he y
-coord
inate
s in
to L
2.
Use
Lin
Reg
(ax +
b)
to d
ete
rmin
e
the s
lop
e-i
nte
rcep
t fo
rm o
f an
equ
ati
on
.
Th
e s
lop
e-i
nte
rcep
t fo
rm o
f th
e e
qu
ati
on
is y =
-0.7
5x -
1.5
or y =
- 3
−
4 x
- 3
−
2 .
Th
is c
an
be r
ew
ritt
en
in
sta
nd
ard
form
as
3x
+ 4y
= -
6.
4-3
Exam
ple
1
Exam
ple
2
Answers (Lesson 4-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
24
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Para
llel
Lin
es
Tw
o n
on
vert
ical
lin
es
are
pa
ra
llel
if t
hey h
ave t
he s
am
e s
lop
e.
All
vert
ical
lin
es
are
para
llel.
W
rit
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses
thro
ug
h (
-1,
6)
an
d i
s p
ara
llel
to t
he g
ra
ph
of y =
2x +
12.
A l
ine p
ara
llel
to y
= 2
x +
12 h
as
the s
am
e s
lop
e,
2.
Rep
lace
m w
ith
2 a
nd
(x
1,
y1)
wit
h
(-1,
6)
in t
he p
oin
t-sl
op
e f
orm
.
y -
y1 =
m(x
- x
1)
Poin
t-slo
pe f
orm
y -
6 =
2(x
- (-
1))
m
= 2
; (x
1,
y1) =
(-
1,
6)
y -
6 =
2(x
+ 1
) S
implif
y.
y -
6 =
2x +
2
Dis
trib
utive P
ropert
y
y =
2x +
8
Slo
pe-inte
rcept
form
Th
ere
fore
, th
e e
qu
ati
on
is
y =
2x +
8.
Exerc
ises
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
ara
llel
to t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
1.
2.
3.
y
= x
- 4
y
= -
1
−
2 x
+ 3
y
= 4
−
3 x
+ 7
4. (-
2,
2),
y =
4x -
2
5. (6
, 4),
y =
1 −
3 x
+ 1
6. (4
, -
2),
y =
-2
x +
3
y
= 4
x +
10
y
= 1
−
3 x
+ 2
y
= -
2x +
6
7. (-
2,
4),
y =
-3
x +
10
8. (-
1,
6),
3x +
y =
12
9. (4
, -
6),
x +
2y =
5
y
= -
3x -
2
y =
-3x +
3
y =
- 1
−
2 x
- 4
10. F
ind
an
equ
ati
on
of
the l
ine t
hat
has
a y
-in
terc
ep
t of
2 t
hat
is p
ara
llel
to t
he g
rap
h o
f th
e l
ine 4
x +
2y =
8.
11. F
ind
an
equ
ati
on
of
the l
ine t
hat
has
a y
-in
terc
ep
t of -
1 t
hat
is p
ara
llel
to t
he g
rap
h o
f th
e l
ine x
- 3
y =
6.
12. F
ind
an
equ
ati
on
of
the l
ine t
hat
has
a y
-in
terc
ep
t of -
4 t
hat
is p
ara
llel
to t
he g
rap
h o
f th
e l
ine y
= 6
.
( –3
, 3
)
x
y
O
4x-
3y=
–1
2
( –8
, 7
)
x
y
O
y=
–1 2
x-
4
2
2
( 5,
1)
x
y
O
y=
x-
8
4-4 Exam
ple
y =
-2x +
2
y =
1
−
3 x
- 1
y =
-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-4
Ch
ap
ter
4
25
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Perp
en
dic
ula
r Lin
es
Tw
o n
on
-vert
ical
lin
es
are
perp
en
dic
ula
r i
f th
eir
slo
pes
are
n
egati
ve r
eci
pro
cals
of
each
oth
er.
Vert
ical
an
d h
ori
zon
tal
lin
es
are
perp
en
dic
ula
r.
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses
thro
ug
h (
-4,
2)
an
d i
s p
erp
en
dic
ula
r t
o t
he g
ra
ph
of
2x -
3y =
9.
Fin
d t
he s
lop
e o
f 2x -
3y =
9.
2
x -
3y =
9
Origin
al equation
-3
y =
-2
x +
9
Subtr
act
2x f
rom
each s
ide.
y =
2 −
3 x
- 3
D
ivid
e e
ach s
ide b
y -
3.
Th
e s
lop
e o
f y =
2 −
3 x
- 3
is
2 −
3 .
So,
the s
lop
e o
f th
e l
ine p
ass
ing t
hro
ugh
(-
4,
2)
that
is
perp
en
dic
ula
r to
th
is l
ine i
s th
e n
egati
ve r
eci
pro
cal
of
2 −
3 ,
or - 3
−
2 .
Use
th
e p
oin
t-sl
op
e f
orm
to f
ind
th
e e
qu
ati
on
.
y -
y1 =
m(x
- x
1)
Poin
t-slo
pe f
orm
y -
2 =
- 3
−
2 (x -
(-
4))
m
= - 3 −
2 ;
(x1,
y1) =
(-
4,
2)
y -
2 =
- 3
−
2 (x +
4)
Sim
plif
y.
y -
2 =
- 3
−
2 x
- 6
D
istr
ibutive P
ropert
y
y =
- 3
−
2 x
- 4
S
lope-inte
rcept
form
Exerc
ises
1. A
RC
HIT
EC
TU
RE
O
n t
he a
rch
itect
’s p
lan
s fo
r a n
ew
hig
h s
chool,
a w
all
rep
rese
nte
d
by −−−
MN
has
en
dp
oin
ts M
(-3, -1) and N(2
, 1). A
wall
rep
rese
nte
d b
y −−−
PQ
has
en
dp
oin
ts
P(4
, -
4)
an
d Q
(-2,
11).
Are
th
e w
all
s p
erp
en
dic
ula
r? E
xp
lain
.
Y
es,
becau
se t
he s
lop
e o
f −
−
MN
2
−
5 i
s t
he n
eg
ati
ve r
ecip
rocal
of
the s
lop
e
of
−−
PQ
(- 5
−
2 ) .
Dete
rm
ine w
heth
er t
he g
ra
ph
s o
f th
e f
oll
ow
ing
eq
ua
tio
ns a
re parallel
or
perpendicular.
Ex
pla
in.
2. 2
x +
y =
-7
, x -
2y =
-4
, 4x -
y =
5 fi
rst
two
are
para
llel
3. y =
3x,
6x -
2y =
7,
3y =
9x -
1 all a
re p
ara
llel
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
erp
en
dic
ula
r t
o t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
4. (4
, 2),
y =
1
−
2 x
+ 1
5. (2
, -
3),
y =
- 2
−
3 x
+ 4
6. (6
, 4),
y =
7x +
1
y
= -
1x +
10
y =
3
−
2 x
- 6
y
= -
1
−
7 x
+ 3
4
−
7
7. (-
8,
-7),
y =
-x -
8
8. (6
, -
2),
y =
-3x -
6
9. (-
5,
-1),
y =
5
−
2 x
- 3
y
= x
+ 1
y
= 1
−
3 x
- 4
y
= -
2
−
5 x
- 3
4-4 Exam
ple
Answers (Lesson 4-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
26
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
ara
llel
to t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
1.
2.
3.
y
= 2
x +
1
y =
-x
y =
1 −
2 x
+ 3
4. (3
, 2),
y =
3x +
4
5. (-
1, -
2),
y =
-3
x +
5
6. (-
1,
1),
y =
x -
4
y
= 3
x -
7
y =
-3x -
5
y =
x +
2
7. (1
, -
3),
y =
-4
x -
1
8. (-
4,
2),
y =
x +
3
9. (-
4,
3),
y =
1 −
2 x
- 6
y
= -
4x +
1
y =
x +
6
y =
1 −
2 x
+ 5
10. R
AD
AR
O
n a
rad
ar
scre
en
, a p
lan
e l
oca
ted
at
A(-
2, 4)
is f
lyin
g t
ow
ard B(4, 3).
An
oth
er
pla
ne,
loca
ted
at
C(-
3, 1), i
s fl
yin
g t
ow
ard D(3, 0). A
re t
he p
lan
es’
path
s p
erp
en
dic
ula
r? E
xp
lain
.
N
o;
the s
lop
es a
re e
qu
al, m
ean
ing
th
e p
ath
s a
re p
ara
llel.
Dete
rm
ine w
heth
er t
he g
ra
ph
s o
f th
e f
oll
ow
ing
eq
ua
tio
ns a
re parallel
or
perpendicular.
Ex
pla
in.
11. y =
2 −
3 x
+ 3, y =
3 −
2 x
, 2x - 3
y =
8
f
irst
an
d t
hir
d a
re p
ara
llel;
slo
pes a
re e
qu
al
12
. y =
4x,
x + 4 y
= 1
2,
4x +
y =
1
f
irst
an
d s
eco
nd
are
perp
en
dic
ula
r; s
lop
es a
re n
eg
ati
ve r
ecip
rocals
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
erp
en
dic
ula
r t
o t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
13. (-
3, -
2),
y =
x +
2
14. (4
, -
1),
y =
2x -
4
15. (-
1, -
6),
x +
3y =
6
y
= -
x -
5
y =
- 1
−
2 x
+ 1
y
= 3
x -
3
16. (-
4,
5),
y =
-4x -
1
17. (-
2,
3),
y = 1
−
4 x
- 4
18. (0
, 0),
y = 1
−
2 x
- 1
y
= 1
−
4 x
+ 6
y
= -
4x -
5
y =
-2x
( –2
, 2
)
x
y O
y=
1 2x+
1
( 1,
–1
)x
y
O
y=
–x+
3
( –2
, –
3)
x
y O
y=
2x-
1
4-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-4
Ch
ap
ter
4
27
Gle
ncoe A
lgeb
ra 1
Practi
ce
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
ara
llel
to t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
1. (3
, 2),
y =
x +
5
2. (-
2,
5),
y =
-4
x +
2
3. (4
, -
6),
y =
- 3 − 4 x
+ 1
y
= x
- 1
y
= -
4x -
3
y =
- 3
−
4 x
- 3
4. (5
, 4),
y =
2 −
5 x
- 2
5. (1
2,
3),
y =
4 −
3 x
+ 5
6. (3
, 1),
2x +
y =
5
y
= 2
−
5 x
+ 2
y
= 4
−
3 x
- 1
3
y =
-2
x +
7
7. (-
3,
4),
3y =
2x -
3
8. (-
1, -
2),
3x -
y =
5
9. (-
8,
2),
5x -
4y =
1
y
= 2
−
3 x
+ 6
y
= 3
x +
1
y =
5 −
4 x
+ 1
2
10. (-
1, -
4),
9x +
3y =
8
11. (-
5,
6),
4x +
3y =
1
12. (3
, 1),
2x +
5y =
7
y
= -
3x -
7
y =
- 4
−
3 x
- 2
−
3
y =
- 2
−
5 x
+ 1
1 −
5
Writ
e a
n e
qu
ati
on
in
slo
pe-i
nte
rcep
t fo
rm
fo
r t
he l
ine t
ha
t p
asses t
hro
ug
h t
he
giv
en
po
int
an
d i
s p
erp
en
dic
ula
r t
o t
he g
ra
ph
of
ea
ch
eq
ua
tio
n.
13. (-
2, -
2),
y =
- 1 − 3 x
+ 9
14. (-
6,
5),
x -
y =
5
15. (-
4, -
3),
4x +
y =
7
y
= 3
x +
4
y =
-x -
1
y =
1 −
4 x
- 2
16. (0
, 1),
x +
5y =
15
17. (2
, 4),
x -
6y =
2
18. (-
1, -
7),
3x +
12y =
-6
y
= 5
x +
1
y =
-6
x +
16
y =
4x -
3
19. (-
4,
1),
4x +
7y =
6
20. (1
0,
5),
5x +
4y =
8
21. (4
, -
5),
2x -
5y =
-10
y
= 7
−
4 x
+ 8
y
= 4
−
5 x
- 3
y
= - 5
−
2 x
+ 5
22. (1
, 1),
3x +
2y =
-7
23. (-
6, -
5),
4x +
3y =
-6
24. (-
3,
5),
5x -
6y =
9
y
= 2
−
3 x
+ 1
−
3
y =
3 −
4 x
- 1
−
2
y =
- 6
−
5 x
+ 7
−
5
25. G
EO
ME
TR
Y Q
uad
rila
tera
l A
BC
D h
as
dia
gon
als
−−
AC
an
d −−−
BD
.
D
ete
rmin
e w
heth
er
−−
AC
is
perp
en
dic
ula
r to
−−−
BD
. E
xp
lain
.
Y
es;
they a
re p
erp
en
dic
ula
r b
ecau
se t
heir
slo
pes a
re
7
an
d - 1
−
7 ,
wh
ich
are
neg
ati
ve r
ecip
rocals
.
26. G
EO
ME
TR
Y T
rian
gle
AB
C h
as
vert
ices
A(0
, 4),
B(1
, 2),
an
d C
(4,
6).
Dete
rmin
e w
heth
er
tria
ngle
AB
C i
s a r
igh
t tr
ian
gle
. E
xp
lain
.
Y
es;
sid
es −−
AB
an
d −−
AC
are
perp
en
dic
ula
r b
ecau
se t
heir
slo
pes a
re -
2
an
d 1
−
2 ,
wh
ich
are
neg
ati
ve r
ecip
rocals
.
x
y O
A
D
C
B
4-4
Answers (Lesson 4-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
28
Gle
ncoe A
lgeb
ra 1
1.B
US
INE
SS
B
rad
y’s
Book
s is
a r
eta
il
store
th
at
als
o s
ell
s book
s on
lin
e.
Th
e
store
’s p
rofi
ts y
are
giv
en
by t
he e
qu
ati
on
y =
2x +
3 w
here
x i
s th
e n
um
ber
of
avail
able
hou
rs f
or
cust
om
er
pu
rch
ase
s.
Bra
dy’s
dis
con
tin
ues
the o
nli
ne s
hop
pin
g
op
tion
. W
rite
a n
ew
equ
ati
on
in
slo
pe-
inte
rcep
t fo
rm t
o s
how
a n
ew
pro
fit
lin
e
wit
h t
he s
am
e p
rofi
t ra
te c
on
tain
ing t
he
poin
t (0
, 0).
2. A
RC
HIT
EC
TU
RE
T
he f
ron
t vie
w o
f a
hou
se i
s d
raw
n o
n g
rap
h p
ap
er.
Th
e l
eft
si
de o
f th
e r
oof
of
the h
ou
se i
s
rep
rese
nte
d b
y t
he e
qu
ati
on
y =
x.
Th
e
roofl
ines
inte
rsect
at
a r
igh
t an
gle
an
d
the p
eak
of
the r
oof
is r
ep
rese
nte
d b
y t
he
poin
t (5
, 5).
Wri
te t
he e
qu
ati
on
in
slo
pe-
inte
rcep
t fo
rm f
or
the l
ine t
hat
create
s th
e r
igh
t si
de o
f th
e r
oof.
y =
-x +
10
3. A
RC
HA
EO
LO
GY
A
n a
rch
aeolo
gis
t is
co
mp
ari
ng t
he l
oca
tion
of
a j
ew
ele
d b
ox
she j
ust
fou
nd
to t
he l
oca
tion
of
a b
rick
w
all
. T
he w
all
can
be r
ep
rese
nte
d b
y t
he
equ
ati
on
y =
- 5
−
3 x
+ 1
3.
Th
e b
ox i
s
lo
cate
d a
t th
e p
oin
t (1
0,
9).
Wri
te a
n
equ
ati
on
rep
rese
nti
ng a
lin
e t
hat
is
perp
en
dic
ula
r to
th
e w
all
an
d t
hat
pass
es
thro
ugh
th
e l
oca
tion
of
the b
ox.
y
= 3
−
5 x
+ 3
4.G
EO
ME
TR
Y A
para
llelo
gra
m i
s cr
eate
d
by t
he i
nte
rsect
ion
s of
the l
ines x
= 2
,
x =
6, y =
1
−
2 x
+ 2
, an
d a
noth
er
lin
e.
Fin
d
th
e e
qu
ati
on
of
the f
ou
rth
lin
e n
eed
ed
to
com
ple
te t
he p
ara
llelo
gra
m.
Th
e l
ine
shou
ld p
ass
th
rou
gh
(2,
0).
(Hint:
Sk
etc
h
a g
rap
h t
o h
elp
you
see t
he l
ines.
)
y =
1 −
2 x
- 1
5
. IN
TE
RIO
R D
ES
IGN
P
am
ela
is
pla
nn
ing
to i
nst
all
an
isl
an
d i
n h
er
kit
chen
. S
he
dra
ws
the s
hap
e s
he l
ikes
by c
on
nect
ing
vert
ices
of
the s
qu
are
til
es
on
her
kit
chen
fl
oor.
Sh
e r
eco
rds
the l
oca
tion
of
each
co
rner
in t
he t
able
.
a.
How
man
y p
air
s of
para
llel
sid
es
are
th
ere
in
th
e s
hap
e s
he d
esi
gn
ed
? E
xp
lain
.
1 p
air
: −−
BC
an
d −
−
AD
are
para
llel
becau
se t
heir
slo
pes a
re b
oth
0.5
.
b.
How
man
y p
air
s of
perp
en
dic
ula
r si
des
are
th
ere
in
th
e s
hap
e s
he
desi
gn
ed
? E
xp
lain
.
2 p
air
s:
−−
BC
⊥ −
−
AB
an
d −
−
AB
⊥ −
−
AD
becau
se −
−
AB
has a
slo
pe o
f -
2,
wh
ich
is t
he o
pp
osit
e r
ecip
rocal
of
the s
lop
es o
f −
−
BC
an
d −
−
AD
, 0.5
.
c.
Wh
at
is t
he s
hap
e o
f h
er
new
isl
an
d?
a t
rap
ezo
id
Wo
rd
Pro
ble
m P
racti
ce
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
y
xO
( 5,
5)
4-4
Co
rner
Dis
tan
ce
fro
m W
est
Wall (
tile
s)
Dis
tan
ce
fro
m S
ou
th
Wall (
tile
s)
A5
4
B3
8
C7
10
D11
7
y =
2x
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-4
Ch
ap
ter
4
29
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Pen
cils o
f Lin
es
All
of
the l
ines
that
pass
th
rou
gh
a s
ingle
poin
t in
th
e s
am
e p
lan
e
are
call
ed
a p
en
cil
of
lin
es.
All
lin
es
wit
h t
he s
am
e s
lop
e,
bu
t d
iffe
ren
t in
terc
ep
ts,
are
als
o
call
ed
a “
pen
cil,
” a p
en
cil
of
pa
ra
llel
lin
es.
Gra
ph
so
me o
f th
e l
ines i
n e
ach
pen
cil
.
1. A
pen
cil
of
lin
es
thro
ugh
th
e
2. A
pen
cil
of
lin
es
desc
ribed
by
poin
t (1
, 3)
y -
4 =
m(x
- 2
), w
here
m i
s an
y
real
nu
mber
3. A
pen
cil
of
lin
es
para
llel
to t
he l
ine
4. A
pen
cil
of
lin
es
desc
ribed
by
x -
2y =
7
y =
mx +
3m
- 2
x
y
Ox
y
O
x
y
Ox
y
O
4-4
Answers (Lesson 4-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
30
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
Invest
igate
Rela
tio
nsh
ips
Usi
ng
Sca
tter
Plo
ts
A s
ca
tter p
lot
is a
gra
ph
in
w
hic
h t
wo s
ets
of
data
are
plo
tted
as
ord
ere
d p
air
s in
a c
oord
inate
pla
ne.
If y
in
crease
s as
x
incr
ease
s, t
here
is
a p
osit
ive c
orrela
tio
n b
etw
een
x a
nd
y.
If y
decr
ease
s as
x i
ncr
ease
s,
there
is
a n
eg
ati
ve c
orrela
tio
n b
etw
een
x a
nd
y.
If x
an
d y
are
not
rela
ted
, th
ere
is
no
co
rrela
tio
n.
EA
RN
ING
S T
he g
ra
ph
at
the r
igh
t
sh
ow
s t
he a
mo
un
t o
f m
on
ey
Ca
rm
en
ea
rn
ed
ea
ch
week
an
d t
he a
mo
un
t sh
e d
ep
osit
ed
in
her s
av
ing
s
acco
un
t th
at
sa
me w
eek
. D
ete
rm
ine w
heth
er t
he
gra
ph
sh
ow
s a
posit
ive c
orrela
tion
, a
neg
ati
ve
correla
tion
, o
r n
o c
orrela
tion
. If
th
ere i
s a
po
sit
ive o
r n
eg
ati
ve c
orrela
tio
n,
describ
e i
ts
mea
nin
g i
n t
he s
itu
ati
on
.
Th
e g
rap
h s
how
s a p
osi
tive c
orr
ela
tion
. T
he m
ore
C
arm
en
earn
s, t
he m
ore
sh
e s
aves.
Exerc
ises
Dete
rm
ine w
heth
er e
ach
gra
ph
sh
ow
s a
posit
ive c
orrela
tion
, a
neg
ati
ve
correla
tion
, o
r n
o c
orrela
tion
. If
th
ere i
s a
po
sit
ive o
r n
eg
ati
ve c
orrela
tio
n,
describ
e i
ts m
ea
nin
g i
n t
he s
itu
ati
on
.
1.
2.
Neg
ati
ve
co
rrela
tio
n;
as t
ime
incre
ases,
sp
eed
d
ecre
ases.
3.
4.
Ave
rage
Wee
kly
Wo
rk H
ou
rs i
n U
.S.
Hours
34.0
34.2
33.8
33.6
34.4
34.6
Yea
rs S
ince
199
5
32
10
54
76
98
Sou
rce:
The W
orld A
lmanac
Ave
rage
Jo
ggin
g Sp
eed
Min
ute
s
Miles per Hour
010
20
515
25
10 5
Car
men
’s E
arn
ings
an
d S
avin
gs
Dollar
s Ea
rned
Dollars Saved
040
80
120
35
30
25
20
15
10 5
no
co
rrela
tio
n
4-5 Exam
ple
Po
sit
ive
co
rrela
tio
n;
as y
ears
in
cre
ase,
the a
vera
ge
weekly
w
ork
ho
urs
als
o
incre
ase.
Po
sit
ive
co
rrela
tio
n;
as y
ears
in
cre
ase,
the a
mo
un
t o
f im
po
rts
als
o
incre
ase.
Ave
rage
U.S
. H
ou
rly
Earn
ings
Hourly Earnings ($)
15 0
16
17
18
19
Yea
rs S
ince
200
3
Sourc
e: U
.S. D
ept.
of
Labor
12
34
5
U.S
. Im
po
rts
fro
m M
exic
o
Imports ($ billions)
130 0
160
190
220
Yea
rs S
ince
200
3
Sourc
e: U
.S. C
ensu
s B
ure
au
12
34
5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-5
Ch
ap
ter
4
31
Gle
ncoe A
lgeb
ra 1
Use
Lin
es
of
Fit
T
he t
ab
le s
ho
ws t
he n
um
ber o
f stu
den
ts p
er c
om
pu
ter i
n E
asto
n
Hig
h S
ch
oo
l fo
r c
erta
in s
ch
oo
l y
ea
rs f
ro
m 1
996 t
o 2
008.
Year
1996
1998
2000
2002
2004
2006
2008
Stu
den
ts p
er
Co
mp
ute
r22
18
14
10
6.1
5.4
4.9
a.
Dra
w a
sca
tter p
lot
an
d d
ete
rm
ine
wh
at
rela
tio
nsh
ip e
xis
ts,
if a
ny
.
Sin
ce y
decr
ease
s as
x i
ncr
ease
s, t
he
corr
ela
tion
is
negati
ve.
b.
Dra
w a
lin
e o
f fi
t fo
r t
he s
ca
tter p
lot.
Dra
w a
lin
e t
hat
pass
es
close
to m
ost
of
the p
oin
ts.
A l
ine o
f fi
t is
sh
ow
n.
c.
Writ
e t
he s
lop
e-i
nte
rcep
t fo
rm
of
an
eq
ua
tio
n
for t
he l
ine o
f fi
t.
Th
e l
ine o
f fi
t sh
ow
n p
ass
es
thro
ugh
(1
999,
16)
an
d (
2005,
5.7
). F
ind
th
e s
lop
e.
m =
5.7
- 1
6
−
20
05
-1999
m =
-1.7
Fin
d b
in
y =
-1.7
x +
b.
16
= -
1.7
· 1
993 +
b
3404
= b
T
here
fore
, an
equ
ati
on
of
a l
ine o
f fi
t is
y =
-1.7
x +
3404.
Exerc
ises
Refe
r t
o t
he t
ab
le f
or E
xercis
es 1
–3.
1. D
raw
a s
catt
er
plo
t.
2. D
raw
a l
ine o
f fi
t fo
r th
e d
ata
.
3. W
rite
th
e s
lop
e-i
nte
rcep
tfo
rm o
f an
equ
ati
on
for
the
lin
e o
f fi
t.
T
he p
oin
ts (
0,
5.0
8)
an
d (
3,
5.8
1)
giv
e
y =
0.2
43x +
5.0
8
as a
lin
e o
f fi
t.
Mo
vie
Ad
mis
sio
n P
rice
s
Admission ($)
5.4
5.6
5.2 5
5.86
6.2
Yea
rs S
ince
199
9
32
15
4
Sou
rce:
U.S
. C
ensus B
ure
au
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
4-5
Stu
den
ts p
er C
om
pu
ter
in E
asto
n H
igh
Sch
oo
l
Students per Computer
8
12
16 4 0
20
24
Yea
r1996
1998
2000
2002
2004
2006
2008
Exam
ple
Years
Sin
ce 1
999
Ad
mis
sio
n
(do
llars
)
0$5.0
8
1$5.3
9
2$5.6
6
3$5.8
1
4$6.0
3
Answers (Lesson 4-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 4 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Sk
ills
Pra
ctic
e
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
Dete
rm
ine w
heth
er e
ach
gra
ph
sh
ow
s a
posit
ive c
orrela
tion
, a
neg
ati
ve
correla
tion
, o
r n
o c
orrela
tion
. If
th
ere i
s a
po
sit
ive o
r n
eg
ati
ve c
orrela
tio
n,
describ
e i
ts m
ea
nin
g i
n t
he s
itu
ati
on
.
1.
2.
P
osit
ive;
the l
on
ger
the e
xerc
ise,
n
o c
orr
ela
tio
n
the m
ore
Calo
ries b
urn
ed
.
3.
4.
N
eg
ati
ve;
as w
eig
ht
incre
ases,
P
osit
ive;
as t
he y
ear
incre
ases,
the n
um
ber
of
rep
eti
tio
ns
the d
eale
rsh
ip’s
reven
ue
decre
ases.
incre
ases
5
. B
AS
EB
ALL
T
he s
catt
er
plo
t sh
ow
s th
e a
vera
ge p
rice
of
a m
ajo
r-le
agu
e b
ase
ball
tic
ket
from
1997 t
o 2
006.
a
. D
ete
rmin
e w
hat
rela
tion
ship
, if
an
y,
exis
ts i
n t
he
data
. E
xp
lain
. P
osit
ive;
as t
he y
ear
incre
ases,
the p
rice i
ncre
ases.
b
. U
se t
he p
oin
ts (
1998,
13.6
0)
an
d (
2003,
19.0
0)
to w
rite
th
e s
lop
e-i
nte
rcep
t fo
rm o
f an
equ
ati
on
for
the l
ine o
f fi
t sh
ow
n i
n t
he s
catt
er
plo
t.
y =
1.0
8x -
2144.2
4
c.
Pre
dic
t th
e p
rice
of
a t
ick
et
in 2
009.
ab
ou
t $25.4
8
Wei
ght-
Lift
ing
Wei
ght
(pounds)
Repetitions
040
8020
6010
012
014
0
14 12 10 8 6 4 2
Lib
rary
Fin
es
Books
Borr
ow
ed
Fines (dollars)
02
45
67
89
13
10
7 6 5 4 3 2 1
Cal
ori
es B
urn
edD
uri
ng
Exer
cise
Tim
e (m
inute
s)
Calories
020
4010
3050
60
600
500
400
300
200
100
4-5
Bas
ebal
l T
ick
et P
rice
s
Average Price ($)
1416 12 018202224
Yea
r
’99
’98
’97
’01
’03
’00
Sourc
e: T
eam
Mar
ketin
g Re
port
, Chi
cago
’02
’04
’05
’06
Car
Dea
lers
hip
Rev
enu
e
Revenue(hundreds of thousands)
46 2 08101214
Yea
r
’99
’01
’03
’00
’02
’04
’05
’06
’07
’08
Ch
ap
ter
4
32
Gle
ncoe A
lgeb
ra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-5
Ch
ap
ter
4
33
Gle
ncoe A
lgeb
ra 1
Pra
ctic
e
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
Dete
rm
ine w
heth
er e
ach
gra
ph
sh
ow
s a
posit
ive c
orrela
tion
, a
neg
ati
ve
correla
tion
, o
r n
o c
orrela
tion
. If
th
ere i
s a
po
sit
ive o
r n
eg
ati
ve c
orrela
tio
n,
describ
e i
ts m
ea
nin
g i
n t
he s
itu
ati
on
.
1.
2.
n
o c
orr
ela
tio
n
3
. D
ISE
AS
E T
he t
able
sh
ow
s th
e n
um
ber
of
case
s of
Food
born
e B
otu
lism
in
th
e U
nit
ed
Sta
tes
for
the
years
2001 t
o 2
005.
a
. D
raw
a s
catt
er
plo
t an
d d
ete
rmin
e w
hat
rela
tion
ship
, if
an
y,
exis
ts i
n t
he d
ata
.
N
eg
ati
ve c
orr
ela
tio
n;
as t
he y
ear
incre
ases,
the n
um
ber
of
cases d
ecre
ases.
b
. D
raw
a l
ine o
f fi
t fo
r th
e s
catt
er
plo
t.
c.
Wri
te t
he s
lop
e-i
nte
rcep
t fo
rm o
f an
equ
ati
on
for
the
lin
e o
f fi
t. S
am
ple
an
sw
er:
y =
-129.7
5x +
906
4
. Z
OO
S T
he t
able
sh
ow
s th
e a
vera
ge a
nd
maxim
um
lo
ngevit
y o
f vari
ou
s an
imals
in
cap
tivit
y.
a
. D
raw
a s
catt
er
plo
t an
d d
ete
rmin
e w
hat
rela
tion
ship
, if
an
y,
exis
ts i
n t
he d
ata
.
P
osit
ive c
orr
ela
tio
n;
as t
he a
vera
ge
incre
ases,
the m
axim
um
in
cre
ases.
b
. D
raw
a l
ine o
f fi
t fo
r th
e s
catt
er
plo
t.
S
am
ple
an
sw
er:
Use (
15,
40),
(35,
70).
c.
Wri
te t
he s
lop
e-i
nte
rcep
t fo
rm o
f an
equ
ati
on
for
the
lin
e o
f fi
t. S
am
ple
an
sw
er:
y =
1.5
x +
17.5
d
. P
red
ict
the m
axim
um
lon
gevit
y f
or
an
an
imal
wit
h
an
avera
ge l
on
gevit
y o
f 33 y
ears
. ab
ou
t 67 y
r
Stat
e El
evat
ion
s
Mea
n E
leva
tion (
feet
)
Highest Point(thousands of feet)
1000
020
0030
00
16 12 8 4
Sou
rce:
U.S
. Geolo
gica
l Surv
ey
Tem
per
atu
re v
ersu
s R
ain
fall
Ave
rage
Annual
Rai
nfa
ll (
inch
es)
AverageTemperature (ºF)
1015
2025
3035
4045
64 60 56 52 0
Sou
rce:
Nat
ional
Oce
anic
and A
tmosp
heric
Adm
inis
trat
ion
4-5
U.S
. Fo
od
bo
rne
Bo
tuli
sm C
ases
Cases
2030 10 04050
Yea
r
2001
2002
2003
2004
Sam
ple
2005
An
imal
Lo
nge
vity
(Y
ears
)
Ave
rage
Maximum
50
1015
2025
3035
4045
80 70 60 50 40 30 20 10
So
urce:
Cente
rs f
or
Dis
eas
e C
ontr
ol
U.S
. F
oo
db
orn
e B
otu
lism
Cases
Year
2001
2002
2003
2004
2005
Cases
39
28
20
16
18
So
urce:
Wal
ker’s
Mam
mal
s of
the W
orld
Lo
ng
evit
y (
years
)
Avg
.12
25
15
835
40
41
20
Max.
47
50
40
20
70
77
61
54
Po
sit
ive;
as t
he m
ean
ele
vati
on
in
cre
ases,
the
hig
hest
po
int
incre
ases.
Answers (Lesson 4-5)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 4 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
4
34
Gle
ncoe A
lgeb
ra 1
1. M
US
IC T
he
scatt
er p
lot
show
s th
e n
um
ber
of
CD
s (i
n m
illi
ons)
th
at
wer
e so
ld f
rom
1999 t
o 2005.
If t
he
tren
d
con
tin
ued
, abou
t h
ow m
an
y C
Ds
wer
e so
ld i
n 2
006?
Sam
ple
an
sw
er:
aro
un
d 7
00 m
illio
n
2. FA
MIL
Y T
he
table
sh
ows
the
pre
dic
ted
an
nu
al
cost
for
a m
idd
le i
nco
me
fam
ily t
o ra
ise
a c
hil
d f
rom
bir
th u
nti
l ad
ult
hoo
d.
Dra
w a
sca
tter
plo
t an
d d
escr
ibe
wh
at
rela
tion
ship
exis
ts w
ith
in t
he
data
.
T
here
is a
po
sit
ive c
orr
ela
tio
n
betw
een
th
e c
hild
’s a
ge a
nd
an
nu
al
co
st.
3. H
OU
SIN
G T
he
med
ian
pri
ce o
f an
ex
isti
ng h
ome
was
$160,0
00 i
n 2
000 a
nd
$240,0
00 i
n 2
007.
If 2
000 r
epre
sen
ts y
ear
0,
use
th
ese
data
poi
nts
to
det
erm
ine
a
pos
sible
lin
e of
bes
t fi
t fo
r th
e tr
end
s in
th
e p
rice
of
exis
tin
g h
omes
. W
rite
th
e eq
uati
on i
n s
lop
e-in
terc
ept
form
.
y
= 4
285.7
x +
110,0
00
4. B
AS
EB
ALL
Th
e ta
ble
sh
ows
the
aver
age
len
gth
(in
min
ute
s) o
f p
rofe
ssio
nal
base
ball
gam
es i
n s
elec
ted
yea
rs.
So
urce:
Elia
s Sport
s B
ure
au
a.
Dra
w a
sca
tter
plo
t an
d d
eter
min
e w
hat
rela
tion
ship
, if
an
y,
exis
ts i
n t
he
data
.
no
co
rrela
tio
n
b.
Exp
lain
wh
at
the
scatt
er p
lot
show
s.
Th
ere
is n
o c
on
sis
ten
t tr
en
d
reg
ard
ing
th
e l
en
gth
of
gam
es.
c.
Dra
w a
lin
e of
fit
for
th
e sc
att
er p
lot.
See l
ine o
f fi
t o
n s
catt
er
plo
t ab
ove.
1992
1990
1994
1998
2000
2002
1996
170
172
168
166
174
180
178
176
Ag
e (
years
)
30
612
15
y
x9
Annual Cost ($1000)
11
12
10 9
13
16
15
14
17
So
urce:The W
orl
d A
lmanac
So
urce:R
IAA
Year
‘01
‘00
‘99
‘03
‘02
‘05
y
x‘04
Millions
750
800
700
650
850
950
900
Wo
rd
Pro
ble
m P
racti
ce
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
4-5
Co
st
of
Rais
ing
a C
hild
Bo
rn i
n 2
003
Ch
ild
’s
Ag
e3
69
12
15
An
nu
al
Co
st
($)
10,7
00
11,7
00
12,6
00
15,0
00
16,7
00
Avera
ge L
en
gth
of
Majo
r L
eag
ue B
aseb
all G
am
es
Year
‘92
‘94
‘96
‘98
‘00
‘02
‘04
Tim
e (
min
)170
174
171
168
178
172
167
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 4-5
Ch
ap
ter
4
35
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Lati
tud
e a
nd
Tem
pera
ture
Th
e latitude o
f a p
lace
on
Eart
h
is t
he
mea
sure
of
its
dis
tan
ce f
rom
the
equ
ato
r. W
hat
do
you
th
ink
is
the
rela
tion
ship
bet
wee
n a
cit
y’s
la
titu
de
an
d i
ts J
an
uary
te
mp
eratu
re?
At
the
righ
t is
a
table
con
tain
ing t
he
lati
tud
es a
nd
Jan
uary
mea
n t
emp
eratu
res
for
fift
een
U.S
. ci
ties
.
Sam
ple
an
sw
ers
are
giv
en
.
So
urces:
Nat
ional
Weat
her
Serv
ice
1. U
se t
he
info
rmati
on i
n t
he
table
to
crea
te
a s
catt
er p
lot
an
d d
raw
a l
ine
of b
est
fit
for
the
data
.
2. W
rite
an
equ
ati
on f
or t
he
lin
e of
fit
. M
ak
e a c
onje
ctu
re a
bou
t th
e re
lati
onsh
ip
bet
wee
n a
cit
y’s
lati
tud
e an
d i
ts m
ean
Jan
uary
tem
per
atu
re.
S
am
ple
an
sw
er:
y =
-2.3
9x +
121.8
6;
Th
e h
igh
er
the
lati
tud
e,
the l
ow
er
the t
em
pera
ture
.
3. U
se y
our
equ
ati
on t
o p
red
ict
the
Jan
uary
mea
n t
emp
eratu
re o
f Ju
nea
u,
Ala
ska,
wh
ich
has
lati
tud
e 58:2
3 N
. -
17.7
º F
4. W
hat
wou
ld y
ou e
xp
ect
to b
e th
e la
titu
de
of a
cit
y w
ith
a J
an
uary
mea
n t
emp
eratu
re
of 1
5°F
? 44:4
2 N
5. W
as
you
r co
nje
ctu
re a
bou
t th
e re
lati
onsh
ip b
etw
een
lati
tud
e an
d t
emp
eratu
re c
orre
ct?
Y
es;
as t
he l
ati
tud
e i
ncre
ases,
the t
em
pera
ture
decre
ases.
6. R
esea
rch
th
e la
titu
des
an
d t
emp
eratu
res
for
citi
es i
n t
he
sou
ther
n h
emis
ph
ere
inst
ead
.
Doe
s you
r co
nje
ctu
re h
old
for
th
ese
citi
es a
s w
ell?
Yes.
Lati
tud
e (ºN
)
Temperature (ºF)
70
60
50
40
30
20
10 0
-10T
L20
40
60
10
30
50
4-5
U.S
. C
ity
Lati
tud
eJan
uary
Mean
Tem
pera
ture
Alb
any,
New
York
42:4
0 N
20.7
°F
Alb
uquerq
ue,
New
Mexic
o35:0
7 N
34.3
°F
Anchora
ge,
Ala
ska
61:1
1 N
14.9
°F
Birm
ingham
, A
labam
a33:3
2 N
41.7
°F
Charlesto
n,
South
Caro
lina
32:4
7 N
47.1
°F
Chic
ago,
Illin
ois
41:5
0 N
21.0
°F
Colu
mbus,
Ohio
39:5
9 N
26.3
°F
Dulu
th,
Min
nesota
46:4
7 N
7.0
°F
Fairbanks,
Ala
ska
64:5
0 N
-10.1
°F
Galv
esto
n,
Texas
29:1
4 N
52.9
°F
Honolu
lu,
Haw
aii
21:1
9 N
72.9
°F
Las V
egas,
Nevada
36:1
2 N
45.1
°F
Mia
mi, F
lorida
25:4
7 N
67.3
°F
Ric
hm
ond,
Virgin
ia37:3
2 N
35.8
°F
Tucson,
Arizona
32:1
2 N
51.3
°F
Answers (Lesson 4-5)
ERROR: undefined
OFFENDING COMMAND: ��
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