Ch.2 Graphs
2.1 TheDistanceandMidpointFormulas
1 RectangularCoordinates
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Namethequadrantinwhichthepointislocated.
1) (8
,
18)
A) I B) II C) III D) IV
2) (–20
,
20)
A) I B) II C) III D) IV
3) (–13
,
–3)
A) I B) II C) III D) IV
4) (18
,
–10)
A) I B) II C) III D) IV
Identifythepointsinthegraphfortheorderedpairs.
x
-5 5
y
5
-5
AB
C
D
E
FG
H
IJK
L
x
-5 5
y
5
-5
AB
C
D
E
FG
H
IJK
L
5) (0,2),(4,3)
A) CandEB)FandEC)BandCD)CandK
6) (–5,–4),(0,–3)
A) IandJB)AandGC)GandID)AandJ
7) (–3,4),(2,0),(4,–5)
A) B,F,andLB)B,C,andLC)F,K,andLD)A,B,andF
8) (3,5),(–3,0)
A) DandGB
)DandJC)IandGD)LandJ
Page1
Givethecoordinatesofthepointsshownonthegraph.
9)
x
-5 5
y
5
-5
A
B
x
-5 5
y
5
-5
A
B
A) A=(7
,
3),B=(–4
,
5) B) A=(3
,
30),B=(5
,
–4)
C) A=(7
,
5),B=(3
,
5) D) A=(7
,
3),B=(5
,
–4)
10)
x
-5 5
y
5
-5
C
D
x
-5 5
y
5
-5
C
D
A) C=(–7
,
4),D=(7
,
–6) B) C=(4
,
–7),D=(–6
,
7)
C) C=(–7
,
–6),D=(4
,
–6) D) C=(–7
,
4),D=(–6
,
7)
11)
x
-5 5
y
5
-5
E
F
x
-5 5
y
5
-5
E
F
A) E=(–2
,
5),F=(–3
,
–6) B) E=(5
,
–2),F=(–6
,
–3)
C) E=(–2
,
–6),F=(5
,
–6) D) E=(–3
,
–6),F=(–2
,
5)
Page2
12)
x
-5 5
y
5
-5
G
H
x
-5 5
y
5
-5
G
H
A) G=(2
,
–2),H=(–3
,
6) B) G=(–2
,
2),H=(6
,
–3)
C) G=(2
,
6),H=(–2
,
6) D) G=(2
,
–2),H=(6
,
–3)
Plotthepointinthexy–plane.Tellinwhichquadrantoronwhataxisthepointlies.
13) (2
,
3)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantI
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantI
Page3
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIV
14) (–2
,
3)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIV
Page4
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantI
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIII
15) (6
,
–2)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIV
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
Page5
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIII
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantI
16) (–3
,
–5)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIII
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIII
Page6
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantIV
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
17) (0,–2)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
y–axis
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
x–axis
Page7
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
y–axis
18) (–4
,
0)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
x–axis
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
y–axis
Page8
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
QuadrantII
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
x–axis
2 UsetheDistanceFormula
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthedistanced(P1,P2)betweenthepointsP1andP2.
1)
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
A) 2 5 B) 2 C) 3 D) 1
2)
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
A) 74 B) 2 6 C) 35 D) 2
Page9
3)
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
A) 2 5 B) 12 3 C) 12 D) 6
4)
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
x
-8 -6 -4 -2 2 4 6 8
y
8
6
4
2
-2
-4
-6
-8
A) 3 10 B) 72 2 C) 72 D) 6
5) P1=(1
,
1);P2=(1
,
–3)
A) 4 B) 2 C) 5 D) 3
6) P1=(3
,
5);P2=(–2
,
17)
A) 13 B) 169 C) 14 D) 26
7) P1=(0,5);P2=(9
,
5)
A) 9 B) 5 C) 106 D) 81
8) P1=(0,0);P2=(6
,
–2)
A) 2 10 B) 40 C) 4 D) 2 3
9) P1=(4
,
6);P2=(–5
,
–2)
A) 145 B) 17 C) 72 D) 1
10) P1=(4
,
–7);P2=(2
,
–1)
A) 2 10 B) 32 2 C) 32 D) 8
Page10
11) P1=(–7
,
–5);P2=(2
,
–2)
A) 3 10 B) 72 2 C) 72 D) 6
12) P1=(–0.8
,
–0.2);P2=(2.6
,
2.8)Roundtothreedecimalplaces,ifnecessary.
A) 4.534 B) 32 C) 14.339 D) 4.634
Decidewhetherornotthepointsaretheverticesofarighttriangle.
13) (4
,
–2),(6
,
–2),(6
,
6)
A) Yes B) No
14) (–9
,
2),(–7
,
6),(–5
,
5)
A) Yes B) No
15) (3
,
7),(9
,
9),(8
,
4)
A) Yes B) No
16) (1
,
1),(7
,
3),(13
,
–4)
A) Yes B) No
Solvetheproblem.
17) Findallvaluesofksothatthegivenpointsare29unitsapart.
(–5,5),(k,0)
A) –3,–7B)
–7C)3,7D)7
18) FindtheareaoftherighttriangleABCwithA=(–2,7),B=(7,–1),C=(3,9).
A) 29squareunits B) 58squareunits C) 58
2
squareunits D) 29
2
squareunits
19) Findallthepointshavinganx–coordinateof9whosedistancefromthepoint(3,–2)is10.
A) (9,6),(9,–10) B) (9,2),(9,–4) C) (9,–12),(9,8) D) (9,13),(9,–7)
20) Amiddleschoolʹsbaseballplayingfieldisasquare,60 feetonaside.Howfarisitdirectlyfromhome
platetosecondbase(thediagonalofthesquare)?Ifnecessary,roundtothenearestfoot.
A) 85feet B) 86feet C) 84 feet D) 92feet
21) Amotorcycleandacarleaveanintersectionatthesametime.Themotorcycleheadsnorthatanaverage
speedof20milesperhour,whilethecarheadseastatanaveragespeedof48milesperhour.Findan
expressionfortheirdistanceapartinmilesattheendofthours.
A) 52tmiles B) t 68miles C) 52 tmiles D) 2t 13miles
22) Arectangularcityparkhasajoggingloopthatgoesalongalength,width,anddiagonalofthepark.Tothe
nearestyard,findthelengthofthejoggingloop,ifthelengthoftheparkis125yardsanditswidthis75
yards.
A) 346yards B) 146yards C) 345yards D) 145yards
Page11
23) FindthelengthofeachsideofthetriangledeterminedbythethreepointsP1
,
P2
,
andP3.Statewhether
thetriangleisanisoscelestriangle,arighttriangle,neitherofthese,orboth.
P1=(–5,–4),P2=(–3,4),P3=(0,–1)
A) d(P1,P2)=217
;d(P2,P3)=34;d(P1,P3)=34
both
B) d(P1,P2)=217
;d(P2,P3)=34;d(P1,P3)=34
isoscelestriangle
C) d(P1,P2)=217
;d(P2,P3)=34;d(P1,P3)=52
righttriangle
D) d(P1,P2)=217
;d(P2,P3)=34;d(P1,P3)=52
neither
3 UsetheMidpointFormula
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
FindthemidpointofthelinesegmentjoiningthepointsP1andP2.
1) P1=(9
,
4);P2=(3
,
6)
A) (6
,
5) B) (12
,
10) C) (6
,
–2) D) (5
,
6)
2) P1=(–5
,
5);P2=(–6
,
–2)
A) –11
2,3
2B) 1
2,7
2C) 1
,
7 D) –11
,
3
3) P1=(7,1);P2=(–16,–16)
A) –9
2,–15
2B) 23
2,17
2C) –9,–15 D) 9,15
4) P1=(0.5
,
–0.4);P2=(–1.7
,
–1.2)
A) (–0.6
,
–0.8) B) (–0.8
,
–0.6) C) (–1.1
,
–0.4) D) (–0.4
,
–1.1)
5) P1=(b
,
5);P2=(0,9)
A) b
2,7 B) b
,
14 C) –b
2,4 D) b
,
7
6) P1=(7b
,
5);P2=(8b
,
8)
A) 15b
2,13
2B) 15b,13 C) b,3 D) 13b
2,15
2
Solvetheproblem.
7) If(2
,
–3)istheendpointofalinesegment,and(4
,
2)isitsmidpoint,findtheotherendpoint.
A) (6
,
7) B) (6
,
–8) C) (–2
,
–13) D) (12
,
1)
8) If(–4
,
5)istheendpointofalinesegment,and(–9
,
2)isitsmidpoint,findtheotherendpoint.
A) (–14
,
–1) B) (–14
,
8) C) (6
,
11) D) (–10
,
–5)
9) If(–7
,
3)istheendpointofalinesegment,and(–5
,
0)isitsmidpoint,findtheotherendpoint.
A) (–3
,
–3) B) (–3
,
6) C) (–11
,
9) D) (–13
,
7)
Page12
10) If(–6
,
–3)istheendpointofalinesegment,and(–9
,
1)isitsmidpoint,findtheotherendpoint.
A) (–12
,
5) B) (–12
,
–7) C) (0
,
–11) D) (2
,
–9)
11) Themediansofatriangleintersectatapoint.Thedistancefromthevertextothepointisexactl
y
two–thirdsofthedistancefromthevertextothemidpointoftheoppositeside.Findtheexactdistanceof
thatpointfromthevertexA(3,4)ofatriangle,giventhattheothertwoverticesareat(0,0)and(8,0).
A) 217
3B) 17
3C) 2 D) 8
3
2.2 GraphsofEquationsinTwoVariables;Intercepts;Symmetry
1 GraphEquationsbyPlottingPoints
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Determinewhetherthegivenpointisonthegraphoftheequation.
1) Equation:y=x2–x
Point:(0,0)
A) Yes B) No
2) Equation:x2+y2=36
Point:(6,0)
A) Yes B) No
Page13
Graphtheequationbyplottingpoints.
3) y=x+6
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page14
4) y=3x+9
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page15
5) y=–x2+9
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page16
6) 4x+5y=20
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page17
7) 4x2+4y=16
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Solvetheproblem.
8) If(a,3)isapointonthegraphofy=2x–5,whatisa?
A) 4 B) 1 C) –1D)
–4
9) If(3,b)isapointonthegraphof3x–2y=17,whatisb?
A) –4B)4 C)
23
3D) 11
3
10) Theheightofabaseball(infeet)attimet(inseconds)isgivenbyy=–16x2+80x+5.Whichoneofthe
followingpointsisnotonthegraphoftheequation?
A) (2,117) B) (1,69) C) (3,101) D) (4,69)
Page18
2 FindInterceptsfromaGraph
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Listtheinterceptsofthegraph.
1)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–3
,
0),(3
,
0) B) (0,–3),(3
,
0) C) (0,–3),(0,3) D) (–3
,
0),(0,3)
2)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A) (0,–1) B) (0,0) C) (–1
,
–1) D) (–1
,
0)
Page19
3)
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
A) –π
2,0 ,(0,5),π
2,0 B) –π
2,0 ,(5,0),π
2,0
C) 0,–π
2,(5,0),0,π
2D) 0,–π
2,(0,5),0,π
2
4)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–2
,
0),(0,8),(4
,
0) B) (–2
,
0),(0,8),(0,4)
C) (0,–2),(8
,
0),(0,4) D) (0,–2),(0,8),(4
,
0)
5)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–2
,
0) B) (0,–2) C) (2
,
0) D) (0,2)
Page20
6)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–8
,
0),(0,–8),(0,8),(8
,
0) B) (–8
,
0),(0,8)
C) (–8
,
0),(0,–8),(0,0),(0,8),(8
,
0) D) (0,8),(8
,
0)
7)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–3
,
0),(1,0)(–5
,
0),(0,–3) B) (–3
,
0),(0,–3),(0,1),(0,–5)
C) (3
,
0),(1,0),(5
,
0),(0,–3) D) (–3
,
0),(0,3),(0,1),(0,5)
8)
A) (–4,0),(0,4),(4,0) B) (–2,0),(0,2),(2,0) C) (–2,0),(0,4),(2,0) D) (–2,0),(2,0)
Page21
3 FindInterceptsfromanEquation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Listtheinterceptsforthegraphoftheequation.
1) y=x+3
A) (–3
,
0),(0,3) B) (3
,
0),(0,–3) C) (–3
,
0),(0,–3) D) (3
,
0),(0,3)
2) y=4x
A) (0,0) B) (0,4) C) (4
,
0) D) (4
,
4)
3) y2=x+16
A) (0,–4),(–16
,
0),(0,4) B) (–4
,
0),(0,–16), (4
,
0)
C) (0,–4),(16
,
0),(0,4) D) (4
,
0),(0,16)
,
(0,–16)
4) y=3x
A) (0,0) B) (1,0) C) (0,1) D) (1,1)
5) x2+y–1=0
A) (–1
,
0),(0,1),(1
,
0) B) (–1
,
0),(0,–1), (1
,
0)
C) (0,–1),(1
,
0),(0,1) D) (1
,
0),(0,1)
,
(0,–1)
6) 4x2+16y2=64
A) (–4
,
0),(0,–2),(0,2),(4
,
0) B) (–2
,
0),(–4
,
0),(4
,
0),(2
,
0)
C) (–16
,
0),(0,–4),(0,4),(16
,
0) D) (–4
,
0),(–16
,
0),(16
,
0),(4
,
0)
7) 16x2+y2=16
A) (–1,0),(0,–4),(0,4),(1,0) B) (–1,0),(0,–16),(0,16),(1,0)
C) (–4
,
0),(0,–1),(0,1),(4
,
0) D) (–16
,
0),(0,–1),(0,1),(16
,
0)
8) y=x3–64
A) (0,–64),(4
,
0) B) (–64
,
0),(0,4) C) (0,–4),(0,4) D) (0,–4),(–4
,
0)
9) y=x4–16
A) (0,–16),(–2
,
0),(2
,
0) B) (0,–16)
C) (0,16),(–2
,
0),(2
,
0) D) (0,16)
10) y=x2+14x+49
A) (–7
,
0),(–7
,
0),(0,49) B) (7
,
0),(7
,
0),(0,49)
C) (0,–7),(0,–7),(49
,
0) D) (0,7),(0,7),(49
,
0)
11) y=x2+25
A) (0,25) B) (0,25),(–5
,
0),(5
,
0)
C) (25
,
0),(0,–5),(0,5) D) (25
,
0)
12) y=3x
x2+9
A) (0,0) B) (–3
,
0),(0,0),(3
,
0)
C) (–9
,
0),(0,0),(9
,
0) D) (0,–3),(0,0),(0,3)
Page22
13) y=x2–16
4x4
A) (–4
,
0),(4
,
0) B) (0,0)
C) (–16
,
0),(0,0),(16
,
0) D) (0,–4),(0,4)
Page23
4 TestanEquationforSymmetrywithRespecttothex–Axis,they–Axis,andtheOrigin
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
PlotthepointA.PlotthepointBthathasthegivensymmetrywithpointA.
1) A=(–4
,
3);BissymmetrictoAwithrespecttothex–axis
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
A)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
B)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
C)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5 A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5 A
B
D)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
Page24
2) A=(0,1);BissymmetrictoAwithrespecttotheorigin
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
A)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
B)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
AB
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
AB
C)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
D)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
A
B
Page25
Listtheinterceptsofthegraph.Tellwhetherthegraphissymmetricwithrespecttothex–axis,y–axis,origin,or
noneofthese.
3)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) intercepts:(–1
,
0)and(1
,
0)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(–1
,
0)and(1
,
0)
symmetricwithrespecttoorigin
C) intercepts:(0,–1)and(0,1)
symmetricwithrespecttox–axis,y–axis,andorigin
D) intercepts:(0,–1)and(0,1)
symmetricwithrespecttoy–axis
4)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) intercepts:(0,4)and(0,–4)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(0,4)and(0,–4)
symmetricwithrespecttoorigin
C) intercepts:(4
,
0)and(–4
,
0)
symmetricwithrespecttox–axis,y–axis,andorigin
D) intercepts:(4
,
0)and(–4
,
0
symmetricwithrespecttoy–axis
Page26
5)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) intercept:(0,7)
nosymmetry
B) intercept:(7
,
0)
nosymmetry
C) intercept:(0,7)
symmetricwithrespecttox–axis
D) intercept:(7
,
0)
symmetricwithrespecttoy–axis
6)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) intercept:(0,4)
symmetricwithrespecttoy–axis
B) intercept:(0,4)
symmetricwithrespecttoorigin
C) intercept:(4
,
0)
symmetricwithrespecttoy–axis
D) intercept:(4
,
0)
symmetricwithrespecttox–axis
Page27
7)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) intercepts:(–3
,
0),(0,0),(3
,
0)
symmetricwithrespecttoorigin
B) intercepts:(–3
,
0),(0,0),(3
,
0)
symmetricwithrespecttox–axis
C) intercepts:(–3
,
0),(0,0),(3
,
0)
symmetricwithrespecttoy–axis
D) intercepts:(–3
,
0),(0,0),(3
,
0)
symmetricwithrespecttox–axis,y–axis,andorigin
Drawacompletegraphsothatithasthegiventypeofsymmetry.
8) Symmetricwithrespecttothey–axis
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
(0, 4)
(2, 0)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
(0, 4)
(2, 0)
Page28
A)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
B)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
C)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
D)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
9) origin
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
Page29
A)
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
B)
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
C)
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
D)
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
––
2
2
y
5
4
3
2
1
-1
-2
-3
-4
-5
10) Symmetricwithrespecttothex–axis
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
(2, 0)
(3, 1)
x
–5–4–3–2–1 12345
y
5
4
3
2
1
-1
-2
-3
-4
-5
(2, 0)
(3, 1)
Page30
A)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
B)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
C)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
D)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
Listtheinterceptsandtype(s)ofsymmetry,ifany.
11) y2=x+1
A) intercepts:(–1
,
0),(0,1),(0,–1)
symmetricwithrespecttox–axis
B) intercepts:(1
,
0),(0,1),(0,–1)
symmetricwithrespecttox–axis
C) intercepts:(0,–1),(1
,
0),(–1
,
0)
symmetricwithrespecttoy–axis
D) intercepts:(0,1),(1
,
0),(–1
,
0)
symmetricwithrespecttoy–axis
12) 9x2+4y2=36
A) intercepts:(2
,
0),(–2
,
0),(0,3),(0,–3)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(3
,
0),(–3
,
0),(0,2),(0,–2)
symmetricwithrespecttox–axisandy–axis
C) intercepts:(2
,
0),(–2
,
0),(0,3),(0,–3)
symmetricwithrespecttox–axisandy–axis
D) intercepts:(3
,
0),(–3
,
0),(0,2),(0,–2)
symmetricwithrespecttotheorigin
Page31
13) y=–x5
x2–7
A) intercept:(0,0)
symmetricwithrespecttoorigin
B) intercepts:(7,0),(–7,0),(0,0)
symmetricwithrespecttoorigin
C) intercept:(0,0)
symmetricwithrespecttox–axis
D) intercept:(0,0)
symmetricwithrespecttoy–axis
Determinewhetherthegraphoftheequationissymmetricwithrespecttothex–axis,they–axis,and/ortheorigin.
14) y=x–6
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
15) y=2x
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
16) x2+y–81=0
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
17) y2–x–4=0
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
18) 4x2+16y2=64
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
19) 16x2+y2=16
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
Page32
20) y=x2+12x+27
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
21) y=9x
x2+81
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
22) y=x2–64
8x4
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
23) y=3x2+3
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
24) y=(x–5)(x+7)
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
25) y=–5x3+4x
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
26) y=–7x4+9x+2
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
Page33
Solvetheproblem.
27) Ifagraphissymmetricwithrespecttothey–axisanditcontainsthepoint(5,–6),whichofthefollowing
pointsisalsoonthegraph?
A) (–5,6) B) (–5,–6) C) (5,–6) D) (–6,5)
28) Ifagraphissymmetricwithrespecttotheoriginanditcontainsthepoint(–4,7),whichofthefollowing
pointsisalsoonthegraph?
A) (4,–7) B) (–4,–7) C) (4,7) D) (7,–4)
5 KnowHowtoGraphKeyEquations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Graphtheequationbyplottingpoints.
1) y=x3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page34
2) x=y2
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page35
3) y=x

x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page36
4) y=1
x
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
B)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
C)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
D)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
Page37
2.3 Lines
1 CalculateandInterprettheSlopeofaLine
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslopeofthelinethroughthepointsandinterprettheslope.
1)
x
-10 -5 5 10
y
10
5
-5
-10
(10, 1)
(0, 0)
x
-10 -5 5 10
y
10
5
-5
-10
(10, 1)
(0, 0)
A) 1
10;forevery10–unitincreaseinx,ywillincreaseby1unit
B) 10;forevery1–unitincreaseinx,ywillincreaseby10 units
C) –1
10;forevery10–unitincreaseinx,ywilldecreaseby1unit
D) –10;forevery1–unitincreaseinx,ywilldecreaseby10 units
Findtheslopeoftheline.
2)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) –6B)
–1
6C) 6 D) 1
6
Page38
3)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) –1 B) 1 C) 3 D) –3
4)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) 1 B) –1C)7 D)
–7
5)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) –1
7B) 1
7C) –7D)7
Findtheslopeofthelinecontainingthetwopoints.
6) (1
,
–9);(–5
,
8)
A) –17
6B) 17
6C) 6
17 D) –6
17
Page39
7) (7
,
0);(0,5)
A) –5
7B) 5
7C) 7
5D) –7
5
8) (6
,
1);(4
,
4)
A) –3
2B) 3
2C) –2
3D) 2
3
9) (–9
,
–8);(–9
,
–6)
A) 2 B) –1
2C) 0 D) undefined
10) (–4
,
–3);(–1
,
–3)
A) 0 B) –1
3C) 3 D) undefined
Page40
2 GraphLinesGivenaPointandtheSlope
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
GraphthelinecontainingthepointPandhavingslopem.
1) P=(–7
,
5);m=–6
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page41
2) P=(–2,–3);m=4
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page42
3) P=(–5
,
–4);m=–2
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page43
4) P=(0,3);m=1
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page44
5) P=(0,2);m=–2
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page45
6) P=(–5
,
0);m=1
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page46
7) P=(4,0);m=–2
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page47
8) P=(–6
,
7);m=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page48
9) P=(–9
,
8);slopeundefined
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
3 FindtheEquationofaVerticalLine
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findanequationforthelinewiththegivenproperties.
1) Slopeundefined;containingthepoint(–10
,
–1)
A) x=–10 B) y=–10 C) x= –1D)y= –1
2) Verticalline;containingthepoint(–5
,
5)
A) x=–5B)y=–5C)x=5D)y=5
Page49
3) Slopeundefined;containingthepoint–1
5,6
A) x=–1
5B) y=6C)y=–1
5D) x=6
4) Verticalline;containingthepoint(2.5
,
–4.4)
A) x=2.5 B) x=–4.4 C) x=0D)x=1.9
4 UsethePoint–SlopeFormofaLine;IdentifyHorizontalLines
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslope–interceptformoftheequationofthelinewiththegivenproperties.
1) Horizontal;containingthepoint(–9
,
9)
A) y=9B)y=–9C)x=9D)x= –9
2) Slope=0;containingthepoint(10
,
1)
A) y=1B)y=10 C) x=1D)x=10
3) Horizontal;containingthepoint–7
8,1
A) y=1B)y=–7
8C) y=0D)y= –1
4) Horizontal;containingthepoint(–2.5
,
5.3)
A) y=5.3 B) y=–2.5 C) y=2.8 D) y=0
Findtheslopeofthelineandsketchitsgraph.
5) y–4=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page50
A) slope=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) slopeisundefined
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) slope=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) slope=1
4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
5 FindtheEquationofaLineGivenTwoPoints
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheequationofthelineinslope–interceptform.
1)
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
A) y=–5x+19 B) y=–1
5x–3
19 C) y= – 5x–9D)y= – 5x–21
Page51
Findanequationfortheline,intheindicatedform,withthegivenproperties.
2) Containingthepoints(–2
,
–5)and(–7
,
5);slope–interceptform
A) y=–2x–9B)y=mx–9C)y+5= – 2(x+2) D) y=2x–9
3) Containingthepoints(2
,
–9)and(–2
,
2);generalform
A) 11x+4y=–14 B) –11x+4y= –14 C) –11x+4y=14 D) 11x–4y=14
4) Containingthepoints(7
,
0)and(0,–4);generalform
A) 4x–7y=28 B) 4x+7y=28 C) y=–4
7x–4D)y=–4
7x+7
5) Containingthepoints(–5
,
3)and(0
,
5);generalform
A) 2x–5y=–25 B) –2x–5y= –25 C) 8x+5y= –25 D) –8x–5y= –25
6) Containingthepoints(7
,
–8)and(0
,
7);generalform
A) 15x+7y=49 B) –15x+7y=49 C) –15x+7y= –49 D) 15x–7y= –49
7) Containingthepoints(–6
,
0)and(–9
,
4);generalform
A) 4x+3y=–24 B) –4x+3y= –24 C) 6x+13y= –106 D) –6x–13y= –106
8) Containingthepoints(–5
,
–2)and(6
,
–6);generalform
A) –4x–11y=42 B) 4x–11y=42 C) 3x–12y= –54 D) –3x+12y= –54
Solve.
9) TherelationshipbetweenCelsius(°C) andFahrenheit(°F) degreesofmeasuringtemperatureislinear.
Findanequationrelating°Cand°Fif10°Ccorrespondsto50°Fand30°Ccorrespondsto86°F.Usethe
equationtofindtheCelsiusmeasureof33°F.
A) C=5
9F–160
9;5
9
°C B) C=5
9F+160
9;325
9
°C
C) C=9
5F–80;–103
5
°C D) C=5
9F–10;25
3
°C
Page52
10) Aschoolhasjustpurchasednewcomputerequipmentfor$19,000.00. Thegraphshowsthedepreciationof
theequipmentover5years.Thepoint(0,19,000)representsthepurchasepriceandthepoint(5,0)
representswhentheequipmentwillbereplaced.Writealinearequationinslope–interceptformthat
relatesthevalueoftheequipment,y,toyearsafterpurchasex.Usetheequationtopredictthevalueofthe
equipmentafter2years.
x
2.5 5
y
25000
22500
20000
17500
15000
12500
10000
7500
5000
2500
x
2.5 5
y
25000
22500
20000
17500
15000
12500
10000
7500
5000
2500
A) y=–3800x+19,000;
valueafter2yearsis$11,400.00;
B) y=19,000x+5;
valueafter2yearsis$11,400.00
C) y=3800x–19,000;
valueafter2yearsis$11,400.00
D) y= – 19,000x+19,000;
valueafter2yearsis$–19,000.00
11) Theaveragevalueofacertaintypeofautomobilewas$14,100 in1993 anddepreciatedto$8580 in1996.
Letybetheaveragevalueoftheautomobileintheyearx,wherex=0represents1993.Writealinear
equationthatrelatestheaveragevalueoftheautomobile,y,totheyearx.
A) y=–1840x+14,100 B) y= –1840x+8580
C) y=–1840x+3060 D) y=–1
1840x–8580
12) Aninvestmentisworth$2680in1991.By1995 ithasgrownto$4384.Letybethevalueoftheinvestment
intheyearx,wherex=0represents1991.Writealinearequationthatrelatesthevalueoftheinvestment,
y,totheyearx.
A) y=426x+2680 B) y=1
426 x+2680 C) y= –426x+6088 D) y= –426x+2680
13) Afaucetisusedtoaddwatertoalargebottlethatalreadycontainedsomewater.Afterithasbeenfilling
for4seconds,thegaugeonthebottleindicatesthatitcontains22ouncesofwater.Afterithasbeenfilling
for11seconds,thegaugeindicatesthebottlecontains57ouncesofwater.Letybetheamountofwaterin
thebottlexsecondsafterthefaucetwasturnedon.Writealinearequationthatrelatestheamountof
waterinthebottle,y,tothetimex.
A) y=5x+2B)y=1
5x+106
5C) y= –5x+42 D) y=5x+46
14) Whenmakingatelephonecallusingacallingcard,acalllasting5 minutescost$1.45.Acalllasting15
minutescost$3.45.Letybethecostofmakingacalllastingxminutesusingacallingcard.Writealinear
equationthatrelatesthecostofamakingacall,y,tothetimex.
A) y=0.2x+0.45 B) y=5x–471
20 C) y= –0.2x+2.45 D) y=0.2x–11.55
Page53
15) Avendorhaslearnedthat,bypricingcarmelapples at$1.00
,
saleswillreach150carmelapples perday.
Raisingthepriceto$1.50willcausethesalestofallto130carmelapplesperday.Letybethenumberof
carmelapplesthevendorsellsatxdollarseach.Writealinearequationthatrelatesthenumberof
carmelapplessoldperday,y,tothepricex.
A) y=–40x+190 B) y=–1
40x+5999
40 C) y=40x+110 D) y= –40x–190
16) Avendorhaslearnedthat,bypricingcaramelapples at$1.25
,
saleswillreach126caramelapples perday.
Raisingthepriceto$2.00willcausethesalestofallto96caramelapplesperday.Letybethenumberof
caramelapplesthevendorsellsatxdollarseach.Writealinearequationthatrelatesthenumberof
caramelapplessoldperdaytothepricex.
A) y=–40x+176 B) y=–1
40x+4031
32 C) y=40x+76 D) y= –40x–176
6 WritetheEquationofaLineinSlope–InterceptForm
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslope–interceptformoftheequationofthelinewiththegivenproperties.
1) Slope=3;containingthepoint(–3
,
–3)
A) y=3x+6B)y=3x–6C)y= –3x–6D)y= –3x+6
2) Slope=0;containingthepoint(–4
,
–1)
A) y=–1B)y=–4C)x= –1D)x= –4
3) Slope=–8;y–intercept=16
A) y=–8x+16 B) y=–8x–16 C) y=16x+8D)y=16x–8
4) x–intercept=5;y–intercept=6
A) y=–6
5x+6B)y=–6
5x+5C)y=6
5x+6D)y=–5
6x+5
Writetheequationinslope–interceptform.
5) 9x+7y=17
A) y=–9
7x+17
7B) y=9
7x+17
7C) y=9x–17 D) y=9
7x–17
7
6) 6x+7y=5
A) y=6
7x+5
7B) y=6x+10 C) y=10
7x+5
7D) y=7
6x–5
6
7) 2x–5y=1
A) y=2
5x–1
5B) y=2
5x+1
5C) y=5
2x+1
2D) y=2x–1
8) x=2y+3
A) y=1
2x–3
2B) y=2x–3C)y=1
2x–3D)y=x–3
2
Page54
Solve.
9) Atruckrentalcompanyrentsamovingtruckonedaybycharging$39 plus$0.07permile.Writealinear
equationthatrelatesthecostC,indollars,ofrentingthetrucktothenumberxofmilesdriven.Whatisthe
costofrentingthetruckifthetruckisdriven190miles?
A) C=0.07x+39;$52.30 B) C=39x+0.07;$7410.07
C) C=0.07x+39;$40.33 D) C=0.07x–39;$25.70
10) Eachweekasoftdrinkmachinesellsxcansofsodafor$0.75/soda.Thecosttotheownerofthesoda
machineforeachsodais$0.10.Theweeklyfixedcostformaintainingthesodamachineis$25/week.Write
anequationthatrelatestheweeklyprofit,P,indollarstothenumberofcanssoldeachweek.Thenusethe
equationtofindtheweeklyprofitwhen92cansofsodaaresoldinaweek.
A) P=0.65x–25;$34.80 B) P=0.65x+25;$84.80
C) P=0.75x–25;$44.00 D) P=0.75x+25;$94.00
11) Eachdaythecommutertraintransportsxpassengerstoorfromthecityat$1.75/passenger.Thedailyfixed
costforrunningthetrainis$1200.Writeanequationthatrelatesthedailyprofit,P,indollarstothe
numberofpassengerseachday.Thenusetheequationtofindthedailyprofitwhenthetrainhas920
passengersinaday.
A) P=1.75x–1200;$410 B) P=1200–1.75x;$410
C) P=1.75x+1200;$2810 D) P=1.75x;$1610
12) Eachmonthabeautysalongivesxmanicuresfor$12.00/manicure.Thecosttotheownerofthebeauty
salonforeachmanicureis$7.35.Themonthlyfixedcosttomaintainamanicurestationis$120.00.Writean
equationthatrelatesthemonthlyprofit,indollars,tothenumberofmanicuresgiveneachmonth.Then
usetheequationtofindthemonthlyprofitwhen200manicuresaregiveninamonth.
A) P=4.65x–120;$810 B) P=12x–120;$2280
C) P=7.35x–120;$1350 D) P=4.65x;$930
13) Eachmonthagasstationsellsxgallonsofgasat$1.92/gallon.Thecosttotheownerofthegasstationfor
eachgallonofgasis$1.32.Themonthlyfixedcostforrunningthegasstationis$37,000.Writeanequation
thatrelatesthemonthlyprofit,indollars,tothenumberofgallonsofgasolinesold.Thenusetheequation
tofindthemonthlyprofitwhen75,000gallonsofgasaresoldinamonth.
A) P=0.60x–37,000;$8000 B) P=1.32x–37,000;$62,000
C) P=1.92x–37,000;$107,000 D) P=0.60x+37,000;$82,000
7 IdentifytheSlopeandy–InterceptofaLinefromItsEquation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslopeandy–interceptoftheline.
1) y=–3
2x–2
A) slope=–3
2;y–intercept=–2 B) slope=–2;y–intercept=–3
2
C) slope=–2
3;y–intercept=2 D) slope=3
2;y–intercept=2
2) x+y=–10
A) slope=–1;y–intercept=–10 B) slope=1;y–intercept=–10
C) slope=0;y–intercept=–10 D) slope= –1;y–intercept=10
Page55
3) 8x+y=–6
A) slope=–8;y–intercept=–6 B) slope=–1
8;y–intercept=–3
4
C) slope=8;y–intercept=–6 D) slope=–4
3;y–intercept=–1
6
4) –6x+7y=1
A) slope=6
7;y–intercept=1
7B) slope=6;y–intercept=10
C) slope=10
7;y–intercept=1
7D) slope=7
6;y–intercept=–1
6
5) 9x+7y=20
A) slope=–9
7;y–intercept=20
7B) slope=9
7;y–intercept=20
7
C) slope=9;y–intercept=20 D) slope=9
7;y–intercept=–20
7
6) 9x–7y=6
A) slope=9
7;y–intercept=–6
7B) slope=9
7;y–intercept=6
7
C) slope=7
9;y–intercept=6
9D) slope=9;y–intercept=6
7) 8x–10y=80
A) slope=4
5;y–intercept=–8 B) slope=–4
5;y–intercept=8
C) slope=5
4;y–intercept=10 D) slope=8;y–intercept=80
8) x+14y=1
A) slope=–1
14;y–intercept=1
14 B) slope=1;y–intercept=1
C) slope=1
14;y–intercept=1
14 D) slope= –14;y–intercept=14
9) –x+10y=90
A) slope=1
10;y–intercept=9 B) slope=–1
10;y–intercept=9
C) slope=–1;y–intercept=90 D) slope=10;y–intercept=–90
10) y=–7
A) slope=0;y–intercept=–7 B) slope= –7;y–intercept=0
C) slope=1;y–intercept=–7 D) slope=0;noy–intercep
t
11) x=5
A) slopeundefined;noy–intercep
t
B) slope=0;y–intercept=5
C) slope=5;y–intercept=0 D) slopeundefined;y–intercept=5
Page56
12) y=–5x
A) slope=–5;y–intercept=0 B) slope=5;y–intercept=0
C) slope=–1
5;y–intercept=0 D) slope=0;y–intercept=–5
8 GraphLinesWritteninGeneralFormUsingIntercepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthegeneralformoftheequationforthelinewiththegivenproperties.
1) Slope=4
5;y–intercept=8
5
A) 4x–5y=–8B)4x+5y= –8C)y=4
5x+8
5D) y=4
5x–8
5
2) Slope=–6
7;containingthepoint(5,2)
A) 6x+7y=44 B) 6x–7y=44 C) 6x+7y= –44 D) 7x+6y= –44
3) Slope=–3
8;containingthepoint(0,3)
A) 3x+8y=24 B) 3x–8y=24 C) 3x+8y= –24 D) 8x+3y= –24
4) Slope=3
7;containing(0,3)
A) –3x+7y=21 B) –3x–7y=21 C) –3x+7y= –21 D) 7x–3y= –21
Findtheslopeofthelineandsketchitsgraph.
5) 3x+4y=25
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page57
A) slope=–3
4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) slope=3
4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) slope=–4
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) slope=4
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
6) 2x–3y=–6
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page58
A) slope=2
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) slope=–2
3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) slope=3
2
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) slope=–3
2
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Solvetheproblem.
7) Findanequationingeneralformforthelinegraphedonagraphingutility.
A) x+2y=–2B)y=–1
2x–1C)2x+y= –1D)y= –2x–1
Page59
9 FindEquationsofParallelLines
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findanequationforthelinewiththegivenproperties.
1) ThesolidlineLcontainsthepoint(2
,
5)andisparalleltothedottedlinewhoseequationisy=2x. Givethe
equationforthelineLinslope–interceptform.
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A) y=2x+1B)y=2x+3C)y–5=2(x–2) D) y=2x+b
2) Paralleltotheliney=3x;containingthepoint(4
,
4)
A) y=3x–8B)y=3x+8C)y–4=3x–4D)y=3x
3) Paralleltothelinex+3y=6;containingthepoint(0,0)
A) y=–1
3xB)y=–1
3x+6C)y=5
3D) y=1
3x
4) Paralleltotheline–3x–y=3;containingthepoint(0,0)
A) y=–3x B) y=1
3x+3C)y=1
3xD)y=–1
3x
5) Paralleltotheliney=–8;containingthepoint(3
,
9)
A) y=9B)y=–9C)y= –8D)y=3
6) Paralleltothelinex=9;containingthepoint(8
,
2)
A) x=8B)x=2C)y=9D)y=2
7) Paralleltotheline2x+7y=72;containingthepoint(8
,
15)
A) 2x+7y=121 B) 2x–7y=121 C) 7x+2y=15 D) 8x+7y=72
8) Paralleltotheline–5x+2y=–2;x–intercept=1
A) –5x+2y=–5B)
–5x+2y=2C)2x+5y=2D)2x+5y=5
Page60
10 FindEquationsofPerpendicularLines
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findanequationforthelinewiththegivenproperties.
1) ThesolidlineLcontainsthepoint(4
,
2)andisperpendiculartothedottedlinewhoseequationisy=2x.
GivetheequationoflineLinslope–interceptform.
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A) y=–1
2x+4B)y–2=–1
2(x–4) C) y=1
2x+4D)y–2=2(x–4)
2) Perpendiculartotheliney=–2x–1;containingthepoint(–3
,
2)
A) y=1
2x+7
2B) y=–1
2x+7
2C) y=2x+7
2D) y=–2x+7
2
3) Perpendiculartotheliney=1
6x+9;containingthepoint(2,–4)
A) y=–6x+8B)y=6x–8C)y= – 6x–8D)y=–1
6x–4
3
4) Perpendiculartotheline–4x–y=3;containingthepoint(0,–3
4)
A) y=1
4x–3
4B) y=1
4x+3C)y=–1
2D) y=–1
4x–3
4
5) Perpendiculartothelinex–7y=5;containingthepoint(4
,
4)
A) y=–7x+32 B) y=7x–32 C) y= – 7x–32 D) y=–1
7x–32
7
6) Perpendiculartotheliney=5;containingthepoint(4
,
3)
A) x=4B)x=3C)y=4D)y=3
7) Perpendiculartothelinex=4;containingthepoint(7
,
1)
A) y=1B)x=1C)y=7D)x=7
8) Perpendiculartotheline4x–5y=–9;containingthepoint(–6
,
3)
A) 5x+4y=–18 B) 5x–4y= –18 C) 4x+5=4D)
–6x+5y= –9
9) Perpendiculartotheline7x–3y=68;containingthepoint(8
,
–8)
A) –3x–7y=32 B) –3x+7y=32 C) 7x+3y=32 D) –3x+7y=68
Page61
10) Perpendiculartotheline–2x+3y=–1;y–intercept=4
A) 3x+2y=8B)
–2x+3y=12 C) 3x+2y=12 D) –2x+3y= –8
Decidewhetherthepairoflinesisparallel,perpendicular,orneither.
11) 3x–2y=–4
2x+3y=5
A) parallel B) perpendicular C) neither
12) 3x–8y=–6
32x+12y=18
A) parallel B) perpendicular C) neither
13) 12x+4y=16
18x+6y=25
A) parallel B) perpendicular C) neither
2.4 Circles
1 WritetheStandardFormoftheEquationofaCircle
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writethestandardformoftheequationofthecircle.
1)
x
y
(4, 6) (8, 6)
x
y
(4, 6) (8, 6)
A) (x–6)2+(y–6)2=4B)(x–6)2+(y–6)2=2
C) (x+6)2+(y+6)2=4D)(x+6)2+(y+6)2=2
Page62
2)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (x–2)2+(y–4)2=16 B) (x+2)2+(y+4)2=16
C) (x–4)2+(y–2)2=16 D) (x+4)2+(y+2)2=16
Writethestandardformoftheequationofthecirclewithradiusrandcenter(h,k).
3) r=4;(h,k)=(0,0)
A) x2+y2=16 B) x2+y2=4
C) (x–4)2+(y–4)2=16 D) (x–4)2+(y–4)2=4
4) r=11;(h,k)=(–9
,
–10)
A) (x+9)2+(y+10)2=121 B) (x–9)2+(y–10)2=121
C) (x+9)2+(y+10)2=11 D) (x–9)2+(y–10)2=11
5) r=12;(h,k)=(–5
,
0)
A) (x+5)2+y2=144 B) (x–5)2+y2=144 C) x2+(y+5)2=12 D) x2+(y–5)2=12
6) r=1;(h,k)=(0,–2)
A) x2+(y+2)2=1B)x
2+(y–2)2=1C
)(x+2)2+y2=1D)(x–2)2+y2=1
7) r=5;(h,k)=(1,8)
A) (x–1)2+(y–8)2=5B)(x+1)2+(y+8)2=5
C) (x–8)2+(y–1)2=25 D) (x+8)2+(y+1)2=25
8) r=10;(h,k)=(0,–1)
A) x2+(y+1)2=10 B) x2+(y–1)2=10 C) (x+1)2+y2=100 D) (x–1)2+y2=100
Solvetheproblem.
9) FindtheequationofacircleinstandardformwhereC(6,–2)andD(–4,4)areendpointsofadiameter.
A) (x–1)2+(y–1)2=34 B) (x+1)2+(y+1)2=34
C) (x–1)2+(y–1)2=136 D) (x+1)2+(y+1)2=136
10) Findtheequationofacircleinstandardformwithcenteratthepoint(–3,2)andtangenttotheliney=4.
A) (x+3)2+(y–2)2=4B)(x+3)2+(y–2)2=16
C) (x–3)2+(y+2)2=4D)(x–3)2+(y+2)2=16
Page63
11) Findtheequationofacircleinstandardformthatistangenttothelinex= –3at(–3,5)andalsotangentto
thelinex=9.
A) (x–3)2+(y–5)2=36 B) (x+3)2+(y–5)2=36
C) (x–3)2+(y+5)2=36 D) (x+3)2+(y+5)2=36
Findthecenter(h,k)andradiusrofthecirclewiththegivenequation.
12) x2+y2=16
A) (h,k)=(0,0);r=4 B) (h,k)=(0,0);r=16
C) (h,k)=(4
,
4);r=4 D) (h,k)=(4
,
4);r=16
13) (x–9)2+(y–3)2=64
A) (h,k)=(9
,
3);r=8 B) (h,k)=(9
,
3);r=64
C) (h,k)=(3
,
9);r=8 D) (h,k)=(3
,
9);r=64
14) (x–10)2+y2=64
A) (h,k)=(10
,
0);r=8 B) (h,k)=(0,10);r=8
C) (h,k)=(0,10);r=64 D) (h,k)=(10
,
0);r=64
15) x2+(y–1)2=64
A) (h,k)=(0,1);r=8 B) (h,k)=(1
,
0);r=8
C) (h,k)=(1
,
0);r=64 D) (h,k)=(0,1);r=64
16) 3(x–5)2+3(y–3)2=18
A) (h,k)=(5,3);r=6B) (h,k)=(5,3);r=36
C) (h,k)=(–5,–3);r=6 D) (h,k)=(–5,–3);r=36
Solvetheproblem.
17) Findthestandardformoftheequationofthecircle.Assumethatthecenterhasintegercoordinatesand
theradiusisaninteger.
A) (x+1)2+(y–2)2=9B)(x–1)2+(y+2)2=9
C) x2+y2+2x–4y–4=0D)x
2+y2–2x+4y–4=0
Page64
2 GraphaCircle
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Graphthecirclewithradiusrandcenter(h,k).
1) r=3;(h,k)=(0,0)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page65
2) r=4;(h,k)=(0,3)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page66
3) r=6;(h,k)=(1
,
0)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page67
4) r=4;(h,k)=(–2
,
–4)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page68
Graphtheequation.
5) x2+y2=16
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page69
6) (x–3)2+(y+3)2=16
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page70
7) x2+(y–1)2=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page71
8) (x–2)2+y2=25
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page72
3 WorkwiththeGeneralFormoftheEquationofaCircle
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthecenter(h,k)andradiusrofthecircle.Graphthecircle.
1) x2+y2–6x–8y+16=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (h,k)=(3
,
4);r=3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) (h,k)=(–3
,
–4);r=3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) (h,k)=(3
,
–4);r=3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) (h,k)=(–3
,
4);r=3
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page73
2) x2+y2+10x+2y+10=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (h,k)=(–5
,
–1);r=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) (h,k)=(5
,
–1);r=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) (h,k)=(5
,
1);r=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) (h,k)=(–5
,
1);r=4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Findthecenter(h,k)andradiusrofthecirclewiththegivenequation.
3) x2+16x+64+(y+4)2=64
A) (h,k)=(–8
,
–4);r=8 B) (h,k)=(–4
,
–8);r=8
C) (h,k)=(8
,
4);r=64 D) (h,k)=(4
,
8);r=64
4) x2–4x+4+y2–10y+25=16
A) (h,k)=(2
,
5);r=4 B) (h,k)=(5
,
2);r=4
C) (h,k)=(–2
,
–5);r=16 D) (h,k)=(–5
,
–2);r=16
5) x2+y2+8x–16y+80=25
A) (h,k)=(–4
,
8);r=5 B) (h,k)=(8
,
–4);r=5
C) (h,k)=(4
,
–8);r=25 D) (h,k)=(–8
,
4);r=25
Page74
6) x2+y2+12x+2y=44
A) (h,k)=(–6
,
–1);r=9 B) (h,k)=(–1
,
–6);r=9
C) (h,k)=(6
,
1);r=81 D) (h,k)=(1
,
6);r=81
7) 4x2+4y2–12x+16y–5=0
A) (h,k)=(3
2,–2);r=30
2B) (h,k)=(–3
2,2);r=30
2
C) (h,k)=(3
2,–2);r=35
2D) (h,k)=(–3
2,2);r=35
2
Findthegeneralformoftheequationofthethecircle.
8) Centeratthepoint(–4,–3);containingthepoint(–3,3)
A) x2+y2+8x+6y–12=0B)x
2+y2+6x+8y–17=0
C) x2+y2–6x+6y–12=0D
)x
2+y2+6x–6y–17=0
9) Centeratthepoint(2,–3);containingthepoint(5,–3)
A) x2+y2–4x+6y+4=0B)x
2+y2+4x–6y+4=0
C) x2+y2–4x+6y+22=0D)x
2+y2+4x–6y+22=0
10) Centeratthepoint(4
,
6);tangenttox–axis
A) x2+y2–8x–12y+16=0B)x
2+y2–8x–12y+36=0
C) x2+y2+8x+12y+16=0D)x
2+y2–8x–12y+88=0
Solvetheproblem.
11) Ifacircleofradius3ismadetorollalongthex–axis,whatistheequationforthepathofthecenterofthe
circle?
A) y=3B)y=0C)y=6D)x=3
12) Earthisrepresentedonamapofthesolarsystemsothatitssurfaceisacirclewiththeequatio
n
x2+y2+4x+2y–3716=0.Aweathersatellitecircles0.7unitsabovetheEarthwiththecenterofits
circularorbitatthecenteroftheEarth.Findthegeneralformoftheequationfortheorbitofthesatelliteon
thismap.
A) x2+y2+4x+2y–3801.89=0B)x
2+y2+4x+2y–55.51=0
C) x2+y2–4x–2y–3801.89=0D)x
2+y2+4x+2y+4.51=0
13) Findanequationofthelinecontainingthecentersofthetwocircles
x2+y2+6x+4y+12=0 and
x2+y2+10x+10y+46=0
A) 3x–2y+5=0B)
–7x+8y+5=0C)3x+2y+5=0D)
–3x–2y+5=0
14) Awildliferesearcherismonitoringablackbearthathasaradiotelemetrycollarwithatransmittingrange
of15miles.Theresearcherisinaresearchstationwithherreceiverandtrackingthebearʹsmovements.If
weputtheoriginofacoordinatesystemattheresearchstation,whatistheequationofallpossible
locationsofthebearwherethetransmitterwouldbeatitsmaximumrange?
A) x2+y2=225 B) x2+y2=30 C) x2+y2=15 D) x2–y2=15
Page75
15) Ifasatelliteisplacedinacircularorbitof380 kilometersabovetheEarth,whatistheequationofthepath
ofthesatelliteiftheoriginisplacedatthecenteroftheEarth(thediameteroftheEarthisapproximately
12,740kilometers)?
A) x2+y2=45,562,500 B) x2+y2=144,400
C) x2+y2=40,576,900 D) x2+y2=172,134,400
16) Apoweroutageaffectedallhomesandbusinesseswithina16 miradiusofthepowerstation.Ifthepower
stationislocated12minorthofthecenteroftown,findanequationofthecircleconsistingofthefurthest
pointsfromthestationaffectedbythepoweroutage.
A) x2+(y–12)2=256 B) x2+(y+12)2=256
C) x2+(y–12)2=16 D) x2+y2=256
17) Apoweroutageaffectedallhomesandbusinesseswithina4 miradiusofthepowerstation.Ifthepower
stationislocated2miwestand3minorthofthecenteroftown,findanequationofthecircleconsistingof
thefurthestpointsfromthestationaffectedbythepoweroutage.
A) (x+2)2+(y–3)2=16 B) (x–2)2+(y–3)2=16
C) (x+2)2+(y+3)2=16 D) (x–2)2+(y+3)2=16
18) AFerriswheelhasadiameterof280feetandthebottomoftheFerriswheelis14feetabovetheground.
Findtheequationofthewheeliftheoriginisplacedonthegrounddirectlybelowthecenterofthewheel,
asillustrated.
280ft.
14ft.
A) x2+(y–154)2=19,600 B) x2+(y–140)2=19,600
C) x2+(y–140)2=78,400 D) x2+y2=19,600
2.5 Variation
1 ConstructaModelUsingDirectVariation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writeageneralformulatodescribethevariation.
1) vvariesdirectlywitht;v=20whent=17
A) v=20
17tB)v=17
20tC)v=20
17t D) v=17
20t
Page76
2) Avariesdirectlywitht2;A=18whent=3
A) A=2t2B) A=6t2C) A=2
t2D) A=6
t2
3) zvariesdirectlywiththesumofthesquaresofxandy;z=10 whenx=6 andy=8
A) z=1
10(x2+y2)B)z
2=x2+y2C) z=1
100 (x2+y2)D)z=1
20(x2+y2)
Ifyvariesdirectlyasx,writeageneralformulatodescribethevariation.
4) y=6whenx=30
A) y=1
5xB)y=5x C) y=x+24 D) y=1
6x
5) y=20whenx=28
A) y=5
7xB)y=7
5xC)y=x–8D)y=4x
6) y=7whenx=1
2
A) y=14x B) y=1
14xC)y=x+13
2D) y=1
7x
7) y=0.8whenx=0.2
A) y=4x B) y=0.2x C) y=x+0.6 D) y=0.25x
8) y=0.3whenx=1.2
A) y=0.25x B) y=0.3x C) y=x–0.9 D) y=4x
Writeageneralformulatodescribethevariation.
9) ThevolumeVofarightcircularconevariesdirectlywiththesquareofitsbaseradiusranditsheighth.
Theconstantofproportionalityis1
3
π.
A) V=1
3
πr2hB)V=1
3
πrh C) V=1
3r2hD)V=1
3
πr2h2
10) ThesurfaceareaSofarightcircularconevariesdirectlyastheradiusrtimesthesquarerootofthesumof
thesquaresofthebaseradiusrandtheheighth.Theconstantofproportionalityisπ.
A) S=πrr
2+h2B) S=πrr
2h2C) S=π r2+h2D) S=πrr
2h
Solvetheproblem.
11) Insimplifiedform,theperiodofvibrationPforapendulumvariesdirectlyasthesquarerootofitslength
L.IfPis1.5sec.whenLis36in.,whatistheperiodwhenthelengthis25in.?
A) 1.25sec B) 6.25 sec C) 20 sec D) 100 sec
12) Theamountofwaterusedtotakeashowerisdirectlyproportionaltotheamountoftimethattheshower
isinuse.Ashowerlasting22minutesrequires4.4gallonsofwater.Findtheamountofwaterusedina
showerlasting4minutes.
A) 0.8gal B) 24.2 gal C) 20 gal D) 1.1gal
Page77
13) Iftheresistanceinanelectricalcircuitisheldconstant,theamountofcurrentflowingthroughthecircuiti
s
directlyproportionaltotheamountofvoltageappliedtothecircuit.When12voltsareappliedtoacircuit,
240milliamperes(mA)ofcurrentflowthroughthecircuit.Findthenewcurrentifthevoltageisincreased
to14volts.
A) 280mA B) 168mA C) 266 mA D) 300 mA
14) Theamountofgasthatahelicopterusesisdirectlyproportionaltothenumberofhoursspentflying.The
helicopterfliesfor2hoursanduses14gallonsoffuel.Findthenumberofgallonsoffuelthatthe
helicopterusestoflyfor6hours.
A) 42gal B) 12gal C) 48 gal D) 49gal
15) Thedistancethatanobjectfallswhenitisdroppedisdirectlyproportionaltothesquareoftheamounto
f
timesinceitwasdropped.Anobjectfalls128feetin2seconds.Findthedistancetheobjectfallsin5
seconds.
A) 800ft B) 160ft C) 320 ft D) 10ft
2 ConstructaModelUsingInverseVariation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writeageneralformulatodescribethevariation.
1) Avariesinverselywithx2;A=8whenx=5
A) A=200
x2B) A=40
x2C) A=8
25x2D) A=40x2
Writeanequationthatexpressestherelationship.Usekastheconstantofvariation.
2) avariesinverselyasz.
A) a=k
zB) a=z
kC) a =kz D) ka=z
3) dvariesinverselyasthesquareoff.
A) d=k
f2B) d=f2
kC) d=k
fD) d=f
k
Ifyvariesinverselyasx,writeageneralformulatodescribethevariation.
4) y=7whenx=3
A) y=21
xB) y=7
3xC)y=x
21 D) y=1
21x
5) y=50whenx=8
A) y=400
xB) y=25
4xC)y=x
400 D) y=1
400x
6) y=42whenx=1
6
A) y=7
xB) y=252x C) y=x
7D) y=1
7x
Page78
7) y=1
6
whenx=12
A) y=2
xB) y=1
72xC)y=x
2D) y=1
2x
8) y=0.2whenx=0.5
A) y=0.1
xB) y=0.4x C) y=10x D) y=10
x
Solvetheproblem.
9) xvariesinverselyasv,andx=14whenv=4.Findxwhenv=8.
A) x=7B)x=16 C) x=28 D) x=2
10) xvariesinverselyasy2,andx=2wheny=8.Findxwheny=2.
A) x=32 B) x=16 C) x=8D)x=4
11) Whenthetemperaturestaysthesame,thevolumeofagasisinverselyproportionaltothepressureofthe
gas.Ifaballoonisfilledwith52cubicinchesofagasatapressureof14poundspersquareinch,findthe
newpressureofthegasifthevolumeisdecreasedto13cubicinches.
A) 56psi B) 13
14
psi C) 42 psi D) 52psi
12) Theamountoftimeittakesaswimmertoswimaraceisinverselyproportionaltotheaveragespeedofthe
swimmer.Aswimmerfinishesaracein200secondswithanaveragespeedof3feetpersecond.Findthe
averagespeedoftheswimmerifittakes120secondstofinishtherace.
A) 5ft/sec B) 6ft/sec C) 7 ft/sec D) 4ft/sec
13) Iftheforceactingonanobjectstaysthesame,thentheaccelerationoftheobjectisinverselyproportional
toitsmass.Ifanobjectwithamassof36kilogramsacceleratesatarateof2meterspersecondpersecond
(m/sec2)byaforce,findtherateofaccelerationofanobjectwithamassof4kilogramsthatispulledby
thesameforce.
A) 18m/sec2B) 2
9
m/sec2C) 16m/sec2D) 9m/sec2
14) Ifthevoltage,V,inanelectriccircuitisheldconstant,thecurrent,I,isinverselyproportionaltothe
resistance,R.Ifthecurrentis240milliamperes(mA)whentheresistanceis5ohms,findthecurrentwhen
theresistanceis30ohms.
A) 40mA B) 1440 mA C) 1434 mA D) 200 mA
15) Whiletravelingataconstantspeedinacar,thecentrifugalaccelerationpassengersfeelwhilethecari
s
turningisinverselyproportionaltotheradiusoftheturn.Ifthepassengersfeelanaccelerationof8feet
persecondpersecond(ft/sec2)whentheradiusoftheturnis90feet,findtheaccelerationthepassengers
feelwhentheradiusoftheturnis180feet.
A) 4ft/sec2B) 5ft/sec2C) 6ft/sec2D) 7ft/sec2
Page79
3 ConstructaModelUsingJointVariationorCombinedVariation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writeageneralformulatodescribethevariation.
1) ThesquareofGvariesdirectlywiththecubeofxandinverselywiththesquareofy;G=3whenx=4 and
y=2
A) G2=9
16
x3
y2B) G2=3
2
x3
y2
C) G2=144y3
x2D) G2=9
256
(x3+y2)
2) Rvariesdirectlywithgandinverselywiththesquareofh;R=3wheng=3andh=5.
A) R=25 g
h2B) R=5g
h2C) R=5h2
gD) R=25gh2
3) zvariesjointlyasthecuberootofxandthesquare ofy;z=25 whenx=125 andy=2.
A) z=5
4
3xy2B) z=4
5
3xy2C) z=20
3x
y2D) z=1
20
3x
y2
4) ThecentrifugalforceFofanobjectspeedingaroundacircularcoursevariesdirectlyastheproductofthe
objectʹsmassmandthesquareofitʹsvelocityvandinverselyastheradiusoftheturnr.
A) F=kmv2
rB) F=kmv
rC) F=km2v
rD) F=kmr
v2
5) Thesafetyloadλofabeamwitharectangularcrosssectionthatissupportedateachendvariesdirectlyas
theproductofthewidthWandthesquareofthedepthDandinverselyasthelengthLofthebeam
betweenthesupports.
A) λ=kWD2
LB) λ=kWD
LC) λ=k(W+D2)
LD) λ=kL
WD2
6) TheilluminationIproducedonasurfacebyasourceoflightvariesdirectlyasthecandlepowercofthe
sourceandinverselyasthesquareofthedistancedbetweenthesourceandthesurface.
A) I=kc
d2B) I=kc2
d2C) I=kcd2D) I=kd2
c
Solvetheproblem.
7) ThevolumeVofagivenmassofgasvariesdirectlyasthetemperatureTandinverselyasthepressureP.
AmeasuringdeviceiscalibratedtogiveV=240in3whenT=160°andP=10lb/in2.Whatisthevolume
onthisdevicewhenthetemperatureis370°andthepressureis25lb/in2?
A) V=222in3B) V=14.8in3C) V=242in3D) V=202in3
8) Thetimeinhoursittakesasatellitetocompleteanorbitaroundtheearthvariesdirectlyastheradiuso
f
theorbit(fromthecenteroftheearth)andinverselyastheorbitalvelocity.Ifasatellitecompletesanorbit
820milesabovetheearthin11hoursatavelocityof31,000mph,howlongwouldittakeasatelliteto
completeanorbitifitisat1300milesabovetheearthatavelocityof26,000mph?(Use3960milesasthe
radiusoftheearth.)
A) 14.43hr B) 20.79 hr C) 3.57 hr D) 144.32 hr
Page80
9) Thepressureofagasvariesjointlyastheamountofthegas(measuredinmoles)andthetemperatureand
inverselyasthevolumeofthegas.Ifthepressureis924kiloPascals(kPa)whenthenumberofmolesis6,
thetemperatureis280°Kelvin,andthevolumeis480cc,findthepressurewhenthenumberofmolesis8,
thetemperatureis320°K,andthevolumeis960cc.
A) 704kPa B) 638kPa C) 1408 kPa D) 1540 kPa
10) Body–massindex,orBMI,takesbothweightandheightintoaccountwhenassessingwhetheran
individualisunderweightoroverweight.BMIvariesdirectlyasoneʹsweight,inpounds,andinverselyas
thesquareofoneʹsheight,ininches.Inadults,normalvaluesfortheBMIarebetween20and25.Aperson
whoweighs182poundsandis70inchestallhasaBMIof26.11.WhatistheBMI,tothenearesttenth,fora
personwhoweighs130poundsandwhois64inchestall?
A) 22.3 B) 22.7 C) 21.9 D) 21.6
11) Theamountofpaintneededtocoverthewallsofaroomvariesjointlyastheperimeteroftheroomand
theheightofthewall.Ifaroomwithaperimeterof65feetand10–footwallsrequires6.5quartsofpaint,
findtheamountofpaintneededtocoverthewallsofaroomwithaperimeterof75feetand10–footwalls.
A) 7.5qt B) 750qt C) 75 qt D) 15qt
12) Thepowerthataresistormustdissipateisjointlyproportionaltothesquareofthecurrentflowing
throughtheresistorandtheresistanceoftheresistor.Ifaresistorneedstodissipate243wattsofpower
when9amperesofcurrentisflowingthroughtheresistorwhoseresistanceis3ohms,findthepowerthat
aresistorneedstodissipatewhen7amperesofcurrentareflowingthrougharesistorwhoseresistanceis
6ohms.
A) 294watts B) 42watts C) 252 watts D) 378 watts
13) Whiletravelinginacar,thecentrifugalforceapassengerexperiencesasthecardrivesinacirclevarie
s
jointlyasthemassofthepassengerandthesquareofthespeedofthecar.Ifapassengerexperiencesa
forceof259.2newtons(N)whenthecarismovingataspeedof60kilometersperhourandthepassenger
hasamassof80kilograms,findtheforceapassengerexperienceswhenthecarismovingat70kilometers
perhourandthepassengerhasamassof40kilograms.
A) 176.4N B) 196N C) 156.8 N D) 245 N
14) Theamountofsimpleinterestearnedonaninvestmentoverafixedamountoftimeisjointlyproportional
totheprincipleinvestedandtheinterestrate.Aprincipleinvestmentof$2400.00withaninterestrateof
2%earned$240.00insimpleinterest.Findtheamountofsimpleinterestearnediftheprincipleis$4900.00
andtheinterestrateis4%.
A) $980.00 B) $98,000.00 C) $490.00 D) $480.00
15) Thevoltageacrossaresistorisjointlyproportionaltotheresistanceoftheresistorandthecurrentflowin
g
throughtheresistor.Ifthevoltageacrossaresistoris45volts(V)foraresistorwhoseresistanceis5ohms
andwhenthecurrentflowingthroughtheresistoris9amperes,findthevoltageacrossaresistorwhose
resistanceis2ohmsandwhenthecurrentflowingthroughtheresistoris3amperes.
A) 6VB)15VC)27VD)18V
Page81
Ch.2 Graphs
AnswerKey
2.1 TheDistanceandMidpointFormulas
1 RectangularCoordinates
2 UsetheDistanceFormula
3 UsetheMidpointFormula
2.2 GraphsofEquationsinTwoVariables;Intercepts;Symmetry
1 GraphEquationsbyPlottingPoints
2 FindInterceptsfromaGraph
3 FindInterceptsfromanEquation
4 TestanEquationforSymmetrywithRespecttothex–Axis,they–Axis,andtheOrigin
5 KnowHowtoGraphKeyEquations
2.3 Lines
1 CalculateandInterprettheSlopeofaLine
2 GraphLinesGivenaPointandtheSlope
3 FindtheEquationofaVerticalLine
4 UsethePoint–SlopeFormofaLine;IdentifyHorizontalLines
6 WritetheEquationofaLineinSlope–InterceptForm
7 IdentifytheSlopeandy–InterceptofaLinefromItsEquation
8 GraphLinesWritteninGeneralFormUsingIntercepts
9 FindEquationsofParallelLines
10 FindEquationsofPerpendicularLines
2.4 Circles
1 WritetheStandardFormoftheEquationofaCircle
2 GraphaCircle
3 WorkwiththeGeneralFormoftheEquationofaCircle
2.5 Variation
1 ConstructaModelUsingDirectVariation
2 ConstructaModelUsingInverseVariation
3 ConstructaModelUsingJointVariationorCombinedVariation
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