Ch.2 Graphs
2.1 TheDistanceandMidpointFormulas
1 RectangularCoordinates
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Namethequadrantinwhichthepointislocated.
1) (11
,
4)
A) I B) II C) III D) IV
2) (–15
,
17)
A) I B) II C) III D) IV
3) (–5
,
–5)
A) I B) II C) III D) IV
4) (14
,
–7)
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
AB
x
-5 5
y
5
-5
AB
A) A=(2
,
4),B=(–4
,
4) B) A=(4
,
20),B=(4
,
–4)
C) A=(2
,
4),B=(4
,
4) D) A=(2
,
4),B=(4
,
–4)
10)
x
-5 5
y
5
-5
C
D
x
-5 5
y
5
-5
C
D
A) C=(–6
,
7),D=(7
,
–6) B) C=(7
,
–6),D=(–6
,
7)
C) C=(–6
,
–6),D=(7
,
–6) D) C=(–6
,
7),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=(–6
,
–5) B) E=(5
,
–2),F=(–5
,
–6)
C) E=(–2
,
–5),F=(5
,
–5) D) E=(–6
,
–5),F=(–2
,
5)
Page2
12)
x
-5 5
y
5
-5
G
H
x
-5 5
y
5
-5
G
H
A) G=(5
,
4),H=(–5
,
6) B) G=(4
,
5),H=(6
,
–5)
C) G=(5
,
6),H=(4
,
6) D) G=(5
,
4),H=(6
,
–5)
Plotthepointinthexy–plane.Tellinwhichquadrantoronwhataxisthepointlies.
13) (1
,
6)
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) (–1
,
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) (1
,
–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) (–6
,
–4)
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,–6)
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) (2
,
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) 34 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) 53 B) 3 5 C) 14 D) 5
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) 4 5 B) 48 3 C) 48 D) 12
5) P1=(4
,
4);P2=(4
,
–5)
A) 9 B) 3 C) 10 D) 8
6) P1=(1
,
–4);P2=(–5
,
–12)
A) 10 B) 100 C) 11 D) 20
7) P1=(0,10);P2=(–8
,
10)
A) 8 B) 10 C) 2 41 D) 64
8) P1=(0,0);P2=(–1
,
–8)
A) 65 B) 65 C) 9 D) 2i 2
9) P1=(1
,
6);P2=(–7
,
–1)
A) 113 B) 15 C) 56 D) 1
10) P1=(3
,
–1);P2=(7
,
–3)
A) 2 5 B) 12 3 C) 12 D) 6
Page10
11) P1=(–3
,
–4);P2=(6
,
2)
A) 3 13 B) 45 5 C) 45 D) 3
12) P1=(–0.1
,
–0.9);P2=(1.5
,
–1.8)Roundtothreedecimalplaces,ifnecessary.
A) 1.836 B) 12.5 C) 5.805 D) 1.936
Decidewhetherornotthepointsaretheverticesofarighttriangle.
13) (3
,
–2),(8
,
–2),(8
,
2)
A) Yes B) No
14) (3
,
–4),(5
,
0),(7
,
–1)
A) Yes B) No
15) (–8
,
5),(–2
,
7),(–3
,
2)
A) Yes B) No
16) (–10
,
–1),(–4
,
1),(2
,
–6)
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=(2
,
1);P2=(8
,
5)
A) (5
,
3) B) (10
,
6) C) (–6
,
–4) D) (3
,
5)
2) P1=(1
,
8);P2=(–9
,
2)
A) –4
,
5 B) 5
,
3 C) 10
,
6 D) –8
,
10
3) P1=(7,1);P2=(–16,–16)
A) –9
2,–15
2B) 23
2,17
2C) –9,–15 D) 9,15
4) P1=(–0.6
,
0.9);P2=(2.6
,
–2.2)
A) (1
,
–0.65) B) (–0.65
,
1) C) (1.6
,
–1.55) D) (–1.55
,
1.6)
5) P1=(b
,
9);P2=(0,3)
A) b
2,6 B) b
,
12 C) –b
2,6 D) b
,
6
6) P1=(3a
,
5);P2=(4a
,
6)
A) 7a
2,11
2B) 7a,11 C) a,1 D) 11a
2,7
2
Solvetheproblem.
7) If(–2
,
–4)istheendpointofalinesegment,and(1
,
–2)isitsmidpoint,findtheotherendpoint.
A) (4
,
0) B) (4
,
–6) C) (–8
,
–8) D) (2
,
2)
8) If(–4
,
2)istheendpointofalinesegment,and(–9
,
–1)isitsmidpoint,findtheotherendpoint.
A) (–14
,
–4) B) (–14
,
5) C) (6
,
8) D) (–10
,
–8)
9) If(–2
,
5)istheendpointofalinesegment,and(2
,
3)isitsmidpoint,findtheotherendpoint.
A) (6
,
1) B) (6
,
7) C) (–10
,
9) D) (–6
,
13)
10) If(8
,
9)istheendpointofalinesegment,and(4
,
12)isitsmidpoint,findtheotherendpoint.
A) (0
,
15) B) (0
,
6) C) (16
,
3) D) (14
,
1)
Page12
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=x3–x
Point:(–4,–66)
A) No B) Yes
2) Equation:x2+y2=4
Point:(2,0)
A) Yes B) No
Page13
Graphtheequationbyplottingpoints.
3) y=x–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
Page14
4) y=2x–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
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+2y=8
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+y=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
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) (–1
,
0),(1
,
0) B) (0,–1),(1
,
0) C) (0,–1),(0,1) D) (–1
,
0),(0,1)
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 ,(0,2),π
2,0 B) –π
2,0 ,(2,0),π
2,0
C) 0,–π
2,(2,0),0,π
2D) 0,–π
2,(0,2),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) (–3
,
0),(0,3),(1
,
0) B) (–3
,
0),(0,3),(0,1)
C) (0,–3),(3
,
0),(0,1) D) (0,–3),(0,3),(1
,
0)
5)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (–1
,
0) B) (0,–1) C) (1
,
0) D) (0,1)
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) (–2
,
0),(1,0)(–5
,
0),(0,–2) B) (–2
,
0),(0,–2),(0,1),(0,–5)
C) (2
,
0),(1,0),(5
,
0),(0,–2) D) (–2
,
0),(0,2),(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+4
A) (–4
,
0),(0,4) B) (4
,
0),(0,–4) C) (–4
,
0),(0,–4) D) (4
,
0),(0,4)
2) y=–4x
A) (0,0) B) (0,–4) C) (–4
,
0) D) (–4
,
–4)
3) y2=x+1
A) (0,–1),(–1
,
0),(0,1) B) (–1
,
0),(0,–1), (1
,
0)
C) (0,–1),(1
,
0),(0,1) D) (1
,
0),(0,1)
,
(0,–1)
4) y=6x
A) (0,0) B) (1,0) C) (0,1) D) (1,1)
5) x2+y–4=0
A) (–2
,
0),(0,4),(2
,
0) B) (–2
,
0),(0,–4), (2
,
0)
C) (0,–2),(4
,
0),(0,2) D) (2
,
0),(0,4)
,
(0,–4)
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) 9x2+y2=9
A) (–1,0),(0,–3),(0,3),(1,0) B) (–1,0),(0,–9),(0,9),(1,0)
C) (–3
,
0),(0,–1),(0,1),(3
,
0) D) (–9
,
0),(0,–1),(0,1),(9
,
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+12x+32
A) (–8
,
0),(–4
,
0),(0,32) B) (8
,
0),(4
,
0),(0,32)
C) (0,–8),(0,–4),(32
,
0) D) (0,8),(0,4),(32
,
0)
11) y=x2+4
A) (0,4) B) (0,4),(–2
,
0),(2
,
0)
C) (4
,
0),(0,–2),(0,2) D) (4
,
0)
12) y=6x
x2+36
A) (0,0) B) (–6
,
0),(0,0),(6
,
0)
C) (–36
,
0),(0,0),(36
,
0) D) (0,–6),(0,0),(0,6)
Page22
13) y=x2–64
8x4
A) (–8
,
0),(8
,
0) B) (0,0)
C) (–64
,
0),(0,0),(64
,
0) D) (0,–8),(0,8)
Page23
4 TestanEquationforSymmetrywithRespecttothex–Axis,they–Axis,andtheOrigin
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
PlotthepointA.PlotthepointBthathasthegivensymmetrywithpointA.
1) A=(5
,
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
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:(–2
,
0)and(2
,
0)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(–2
,
0)and(2
,
0)
symmetricwithrespecttoorigin
C) intercepts:(0,–2)and(0,2)
symmetricwithrespecttox–axis,y–axis,andorigin
D) intercepts:(0,–2)and(0,2)
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:(0,1)and(0,–1)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(0,1)and(0,–1)
symmetricwithrespecttoorigin
C) intercepts:(1
,
0)and(–1
,
0)
symmetricwithrespecttox–axis,y–axis,andorigin
D) intercepts:(1
,
0)and(–1
,
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:(0,8)
nosymmetry
B) intercept:(8
,
0)
nosymmetry
C) intercept:(0,8)
symmetricwithrespecttox–axis
D) intercept:(8
,
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:(0,5)
symmetricwithrespecttoy–axis
B) intercept:(0,5)
symmetricwithrespecttoorigin
C) intercept:(5
,
0)
symmetricwithrespecttoy–axis
D) intercept:(5
,
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:(–2
,
0),(0,0),(2
,
0)
symmetricwithrespecttoorigin
B) intercepts:(–2
,
0),(0,0),(2
,
0)
symmetricwithrespecttox–axis
C) intercepts:(–2
,
0),(0,0),(2
,
0)
symmetricwithrespecttoy–axis
D) intercepts:(–2
,
0),(0,0),(2
,
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, 2)
(2, –2)
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
(0, 2)
(2, –2)
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) 16x2+y2=16
A) intercepts:(1
,
0),(–1
,
0),(0,4),(0,–4)
symmetricwithrespecttox–axis,y–axis,andorigin
B) intercepts:(4
,
0),(–4
,
0),(0,1),(0,–1)
symmetricwithrespecttox–axisandy–axis
C) intercepts:(1
,
0),(–1
,
0),(0,4),(0,–4)
symmetricwithrespecttox–axisandy–axis
D) intercepts:(4
,
0),(–4
,
0),(0,1),(0,–1)
symmetricwithrespecttotheorigin
Page31
13) y=–x5
x2–9
A) intercept:(0,0)
symmetricwithrespecttoorigin
B) intercepts:(3
,
0),(–3
,
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–1
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–36=0
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
17) y2–x–25=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) 9x2+y2=9
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
Page32
20) y=x2+15x+56
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
21) y=5x
x2+25
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
22) y=x2–49
7x4
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
23) y=2x2–1
A) y–axis
B) x–axis
C) origin
D) x–axis,y–axis,origin
E) none
24) y=(x–9)(x+4)
A) x–axis
B) y–axis
C) origin
D) x–axis,y–axis,origin
E) none
25) y=–8x3+4x
A) origin
B) x–axis
C) y–axis
D) x–axis,y–axis,origin
E) none
26) y=–7x4+7x+9
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
(3, 1)
(0, 0)
x
-10 -5 5 10
y
10
5
-5
-10
(3, 1)
(0, 0)
A) 1
3;forevery3–unitincreaseinx,ywillincreaseby1unit
B) 3;forevery1–unitincreaseinx,ywillincreaseby3 units
C) –1
3;forevery3–unitincreaseinx,ywilldecreaseby1unit
D) –3;forevery1–unitincreaseinx,ywilldecreaseby3 units
Findtheslopeoftheline.
2)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) 7 B) 1
7C) –7D)
–1
7
Page38
3)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) –1B)1 C)
–3D)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)
–7D)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) 7 D) –7
Findtheslopeofthelinecontainingthetwopoints.
6) (4
,
–9);(–3
,
6)
A) –15
7B) 15
7C) 7
15 D) –7
15
Page39
7) (8
,
0);(0,5)
A) –5
8B) 5
8C) 8
5D) –8
5
8) (–3
,
–4);(–6
,
–5)
A) 1
3B) –1
3C) 3 D) –3
9) (–3
,
–2);(–3
,
–1)
A) 1 B) –1 C) 0 D) undefined
10) (–8
,
–3);(4
,
–3)
A) 0 B) –1
12 C) 12 D) undefined
Page40
2 GraphLinesGivenaPointandtheSlope
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
GraphthelinecontainingthepointPandhavingslopem.
1) P=(4,6);m=–13
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
Page41
2) P=(–5
,
–8);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
Page42
3) P=(–3,–10);m=–1
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=(0,5);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=–1
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
Page45
6) P=(–4
,
0);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
Page46
7) P=(6
,
0);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
Page47
8) P=(6
,
9);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=(–1
,
–10);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(–5
,
–6)
A) x=–5B)y=–5C)x= –6D)y= –6
2) Verticalline;containingthepoint(1
,
–2)
A) x=1B)y=1C)x= –2D)y= –2
Page49
3) Slopeundefined;containingthepoint–3
4,7
A) x=–3
4B) y=7C)y=–3
4D) x=7
4) Verticalline;containingthepoint(2.1
,
2.6)
A) x=2.1 B) x=2.6 C) x=0D)x=4.7
4 UsethePoint–SlopeFormofaLine;IdentifyHorizontalLines
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslope–interceptformoftheequationofthelinewiththegivenproperties.
1) Horizontal;containingthepoint(9
,
–10)
A) y=–10 B) y=9C)x= –10 D) x=9
2) Slope=0;containingthepoint(–6
,
–5)
A) y=–5B)y=–6C)x= –5D)x= –6
3) Horizontal;containingthepoint–1
9,7
A) y=7B)y=–1
9C) y=0D)y= –7
4) Horizontal;containingthepoint(5.2
,
–4.9)
A) y=–4.9 B) y=5.2 C) y=0.3 D) y=0
Findtheslopeofthelineandsketchitsgraph.
5) y–5=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=5
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) slope=1
5
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=–2x–5B)y=–1
2x–7
5C) y= – 2x+2D)y= – 2x+5
Page51
Findanequationfortheline,intheindicatedform,withthegivenproperties.
2) Containingthepoints(4
,
1)and(2
,
–4);slope–interceptform
A) y=5
2x–9B)y=mx–9C)y–1=5
2(x–4) D) y=–5
2x–9
3) Containingthepoints(1
,
–8)and(–4
,
3);generalform
A) 11x+5y=–29 B) –11x+5y= –29 C) –9x+7y=15 D) 9x–7y=15
4) Containingthepoints(8
,
0)and(0,–12);generalform
A) 12x–8y=96 B) 12x+8y=96 C) y=–3
2x–12 D) y=–3
2x+8
5) Containingthepoints(6
,
4)and(2
,
9);generalform
A) 5x+4y=46 B) –5x+4y=46 C) –2x+7y= –67 D) 2x–7y= –67
6) Containingthepoints(–2
,
6)and(0
,
9);generalform
A) 3x–2y=–18 B) –3x–2y= –18 C) 8x+9y= –81 D) –8x–9y= –81
7) Containingthepoints(–8
,
0)and(4
,
–5);generalform
A) –5x–12y=40 B) 5x–12y=40 C) 8x–9y= –13 D) –8x+9y= –13
8) Containingthepoints(6
,
–5)and(–3
,
3);generalform
A) 8x+9y=3B)
–8x+9y=3C)
–11x+6y=15 D) 11x–6y=15
Solve.
9) TherelationshipbetweenCelsius(°C) andFahrenheit(°F) degreesofmeasuringtemperatureislinear.
Findanequationrelating°Cand°Fif10°Ccorrespondsto50°Fand30°Ccorrespondsto86°F.Usethe
equationtofindtheCelsiusmeasureof20°F.
A) C=5
9F–160
9;–20
3
°C B) C=5
9F+160
9;260
9
°C
C) C=9
5F–80;–44°C D) C=5
9F–10;10
9
°C
Page52
10) Aschoolhasjustpurchasednewcomputerequipmentfor$19,000.00. Thegraphshowsthedepreciationof
theequipmentover5years.Thepoint(0,19,000)representsthepurchasepriceandthepoint(5,0)
representswhentheequipmentwillbereplaced.Writealinearequationinslope–interceptformthat
relatesthevalueoftheequipment,y,toyearsafterpurchasex.Usetheequationtopredictthevalueofthe
equipmentafter1years.
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;
valueafter1yearsis$15,200.00;
B) y=19,000x+5;
valueafter1yearsis$15,200.00
C) y=3800x–19,000;
valueafter1yearsis$15,200.00
D) y= – 19,000x+19,000;
valueafter1yearsis$0.00
11) Theaveragevalueofacertaintypeofautomobilewas$13,980 in1995 anddepreciatedto$4500 in2000.
Letybetheaveragevalueoftheautomobileintheyearx,wherex=0represents1995.Writealinear
equationthatrelatestheaveragevalueoftheautomobile,y,totheyearx.
A) y=–1896x+13,980 B) y= –1896x+4500
C) y=–1896x–4980 D) y=–1
1896x–4500
12) Aninvestmentisworth$3765in1994.By1997 ithasgrownto$4338.Letybethevalueoftheinvestment
intheyearx,wherex=0represents1994.Writealinearequationthatrelatesthevalueoftheinvestment,
y,totheyearx.
A) y=191x+3765 B) y=1
191 x+3765 C) y= –191x+4911 D) y= –191x+3765
13) Afaucetisusedtoaddwatertoalargebottlethatalreadycontainedsomewater.Afterithasbeenfilling
for3seconds,thegaugeonthebottleindicatesthatitcontains11ouncesofwater.Afterithasbeenfilling
for11seconds,thegaugeindicatesthebottlecontains27ouncesofwater.Letybetheamountofwaterin
thebottlexsecondsafterthefaucetwasturnedon.Writealinearequationthatrelatestheamountof
waterinthebottle,y,tothetimex.
A) y=2x+5B)y=1
2x+19
2C) y= –2x+17 D) y=2x+16
14) Whenmakingatelephonecallusingacallingcard,acalllasting5 minutescost$0.95.Acalllasting14
minutescost$1.85.Letybethecostofmakingacalllastingxminutesusingacallingcard.Writealinear
equationthatrelatesthecostofamakingacall,y,tothetimex.
A) y=0.1x+0.45 B) y=10x–981
20 C) y= –0.1x+1.45 D) y=0.1x–12.15
Page53
15) Avendorhaslearnedthat,bypricinghotdogs at$1.25
,
saleswillreach107 hotdogsperday.Raisingthe
priceto$2.00willcausethesalestofallto68hotdogsperday.Letybethenumberofhotdogsthe
vendorsellsatxdollarseach.Writealinearequationthatrelatesthenumberofhotdogssoldperday,y,
tothepricex.
A) y=–52x+172 B) y=–1
52x+22251
208 C) y=52x+42 D) y= –52x–172
16) Avendorhaslearnedthat,bypricingcaramelapples at$1.50
,
saleswillreach112caramelapples perday.
Raisingthepriceto$2.25willcausethesalestofallto73caramelapplesperday.Letybethenumberof
caramelapplesthevendorsellsatxdollarseach.Writealinearequationthatrelatesthenumberof
caramelapplessoldperdaytothepricex.
A) y=–52x+190 B) y=–1
52x+11645
104 C) y=52x+34 D) y= –52x–190
6 WritetheEquationofaLineinSlope–InterceptForm
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findtheslope–interceptformoftheequationofthelinewiththegivenproperties.
1) Slope=5;containingthepoint(–2
,
–5)
A) y=5x+5B)y=5x–5C)y= –5x–5D)y= –5x+5
2) Slope=0;containingthepoint(–6
,
–3)
A) y=–3B)y=–6C)x= –3D)x= –6
3) Slope=2;y–intercept=–8
A) y=2x–8B)y=2x+8C)y= –8x–2D)y= –8x+2
4) x–intercept=3;y–intercept=5
A) y=–5
3x+5B)y=–5
3x+3C)y=5
3x+5D)y=–3
5x+3
Writetheequationinslope–interceptform.
5) 11x+2y=17
A) y=–11
2x+17
2B) y=11
2x+17
2C) y=11x–17 D) y=11
2x–17
2
6) 6x+7y=3
A) y=6
7x+3
7B) y=6x+10 C) y=10
7x+3
7D) y=7
6x–3
6
7) 3x–5y=9
A) y=3
5x–9
5B) y=3
5x+9
5C) y=5
3x+9
3D) y=3x–9
8) x=7y+6
A) y=1
7x–6
7B) y=7x–6C)y=1
7x–6D)y=x–6
7
Page54
Solve.
9) Atruckrentalcompanyrentsamovingtruckonedaybycharging$31 plus$0.09permile.Writealinear
equationthatrelatesthecostC,indollars,ofrentingthetrucktothenumberxofmilesdriven.Whatisthe
costofrentingthetruckifthetruckisdriven210miles?
A) C=0.09x+31;$49.90 B) C=31x+0.09;$6510.09
C) C=0.09x+31;$32.89 D) C=0.09x–31;$12.10
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=7
4x–4
A) slope=7
4;y–intercept=–4 B) slope=–4;y–intercept=7
4
C) slope=4
7;y–intercept=4 D) slope=–7
4;y–intercept=4
2) x+y=–6
A) slope=–1;y–intercept=–6 B) slope=1;y–intercept=–6
C) slope=0;y–intercept=–6 D) slope= –1;y–intercept=6
Page55
3) 5x+y=8
A) slope=–5;y–intercept=8 B) slope=–1
5;y–intercept=8
5
C) slope=5;y–intercept=8 D) slope=5
8;y–intercept=1
8
4) –6x+7y=10
A) slope=6
7;y–intercept=10
7B) slope=6;y–intercept=12
C) slope=12
7;y–intercept=10
7D) slope=7
6;y–intercept=–10
6
5) 2x+9y=19
A) slope=–2
9;y–intercept=19
9B) slope=2
9;y–intercept=19
9
C) slope=2;y–intercept=19 D) slope=2
9;y–intercept=–19
9
6) 7x–6y=5
A) slope=7
6;y–intercept=–5
6B) slope=7
6;y–intercept=5
6
C) slope=6
7;y–intercept=5
7D) slope=7;y–intercept=5
7) 12x–3y=36
A) slope=4;y–intercept=–12 B) slope= – 4;y–intercept=12
C) slope=1
4;y–intercept=3 D) slope=12;y–intercept=36
8) x+11y=1
A) slope=–1
11;y–intercept=1
11 B) slope=1;y–intercept=1
C) slope=1
11;y–intercept=1
11 D) slope= –11;y–intercept=11
9) –x+7y=84
A) slope=1
7;y–intercept=12 B) slope=–1
7;y–intercept=12
C) slope=–1;y–intercept=84 D) slope=7;y–intercept=–84
10) y=–5
A) slope=0;y–intercept=–5 B) slope= –5;y–intercept=0
C) slope=1;y–intercept=–5 D) slope=0;noy–intercep
t
11) x=–1
A) slopeundefined;noy–intercep
t
B) slope=0;y–intercept=–1
C) slope=–1;y–intercept=0 D) slopeundefined;y–intercept= –1
Page56
12) y=4x
A) slope=4;y–intercept=0 B) slope= –4;y–intercept=0
C) slope=1
4;y–intercept=0 D) slope=0;y–intercept=4
8 GraphLinesWritteninGeneralFormUsingIntercepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthegeneralformoftheequationforthelinewiththegivenproperties.
1) Slope=3
5;y–intercept=4
5
A) 3x–5y=–4B)3x+5y= –4C)y=3
5x+4
5D) y=3
5x–4
5
2) Slope=–3
5;containingthepoint(5,2)
A) 3x+5y=25 B) 3x–5y=25 C) 3x+5y= –25 D) 5x+3y= –25
3) Slope=–5
9;containingthepoint(0,3)
A) 5x+9y=27 B) 5x–9y=27 C) 5x+9y= –27 D) 9x+5y= –27
4) Slope=2
9;containing(0,2)
A) –2x+9y=18 B) –2x–9y=18 C) –2x+9y= –18 D) 9x–2y= –18
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) 4x–5y=2
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Page58
A) slope=4
5
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) slope=–4
5
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) slope=5
4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) slope=–5
4
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
,
1)andisparalleltothedottedlinewhoseequationisy=2x. Givethe
equationforthelineLinslope–interceptform.
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A) y=2x–3B)y=2x–1C)y–1=2(x–2) D) y=2x+b
2) Paralleltotheliney=–4x;containingthepoint(2
,
3)
A) y=–4x+11 B) y=–4x–11 C) y–3= –4x–2D)y= –4x
3) Paralleltothelinex+5y=3;containingthepoint(0,0)
A) y=–1
5xB)y=–1
5x+3C)y=2
5D) y=1
5x
4) Paralleltotheline–2x–y=4;containingthepoint(0,0)
A) y=–2x B) y=1
2x+4C)y=1
2xD)y=–1
2x
5) Paralleltotheliney=–6;containingthepoint(8
,
2)
A) y=2B)y=–2C)y= –6D)y=8
6) Paralleltothelinex=–6;containingthepoint(4
,
3)
A) x=4B)x=3C)y= –6D)y=3
7) Paralleltotheline2x+7y=35;containingthepoint(7
,
12)
A) 2x+7y=98 B) 2x–7y=98 C) 7x+2y=12 D) 7x+7y=35
8) Paralleltotheline–3x–5y=–5;x–intercept=2
A) –3x–5y=–6B)
–3x–5y= –10 C) –5x+3y= –10 D) –5x+3y=6
Page60
10 FindEquationsofPerpendicularLines
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findanequationforthelinewiththegivenproperties.
1) ThesolidlineLcontainsthepoint(3
,
2)andisperpendiculartothedottedlinewhoseequationisy=2x.
GivetheequationoflineLinslope–interceptform.
x
-5 5
y
5
-5
x
-5 5
y
5
-5
A) y=–1
2x+7
2B) y–2=–1
2(x–3) C) y=1
2x+7
2D) y–2=2(x–3)
2) Perpendiculartotheliney=2x+1;containingthepoint(–4
,
–1)
A) y=–1
2x–3B)y=1
2x–3C)y= –2x–3D)y=2x–3
3) Perpendiculartotheliney=1
7x+8;containingthepoint(3,–2)
A) y=–7x+19 B) y=7x–19 C) y= – 7x–19 D) y=–1
7x–19
7
4) Perpendiculartotheline–2x–y=6;containingthepoint(0,–3)
A) y=1
2x–3B)y=1
2x+6C)y=–5
2D) y=–1
2x–3
5) Perpendiculartothelinex–7y=6;containingthepoint(4
,
4)
A) y=–7x+32 B) y=7x–32 C) y= – 7x–32 D) y=–1
7x–32
7
6) Perpendiculartotheliney=8;containingthepoint(2
,
3)
A) x=2B)x=3C)y=2D)y=3
7) Perpendiculartothelinex=–4;containingthepoint(3
,
8)
A) y=8B)x=8C)y=3D)x=3
8) Perpendiculartotheline–9x–7y=–82;containingthepoint(6
,
–4)
A) 7x–9y=78 B) 7x+9y=78 C) –9x+7= –9D)6x+7y= –82
9) Perpendiculartotheline–7x+4y=–15;containingthepoint(5
,
6)
A) 4x+7y=62 B) 4x–7y=62 C) –7x–4y=62 D) 4x–7y= –15
10) Perpendiculartotheline–2x–3y=–6;y–intercept= –4
A) –3x+2y=–8B)
–2x–3y=12 C) –3x+2y=12 D) –2x–3y=8
Page61
Decidewhetherthepairoflinesisparallel,perpendicular,orneither.
11) 3x–4y=–4
8x+6y=–11
A) parallel B) perpendicular C) neither
12) 3x–4y=16
8x+6y=–4
A) parallel B) perpendicular C) neither
13) 12x+4y=16
18x+6y=26
A) parallel B) perpendicular C) neither
2.4 Circles
1 WritetheStandardFormoftheEquationofaCircle
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writethestandardformoftheequationofthecircle.
1)
x
y
(3, 6) (7, 6)
x
y
(3, 6) (7, 6)
A) (x–5)2+(y–6)2=4B)(x–5)2+(y–6)2=2
C) (x+5)2+(y+6)2=4D)(x+5)2+(y+6)2=2
2)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (x–4)2+(y–1)2=16 B) (x+4)2+(y+1)2=16
C) (x–1)2+(y–4)2=16 D) (x+1)2+(y+4)2=16
Page62
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=4;(h,k)=(3
,
–5)
A) (x–3)2+(y+5)2=16 B) (x+3)2+(y–5)2=16
C) (x–3)2+(y+5)2=4D)(x+3)2+(y–5)2=4
5) r=6;(h,k)=(6
,
0)
A) (x–6)2+y2=36 B) (x+6)2+y2=36 C) x2+(y–6)2=6D)x
2+(y+6)2=6
6) r=6;(h,k)=(0,10)
A) x2+(y–10)2=36 B) x2+(y+10)2=6C)(x–10)2+y2=36 D) (x+10)2+y2=36
7) r=19;(h,k)=(8,–8)
A) (x–8)2+(y+8)2=19 B) (x+8)2+(y–8)2=19
C) (x+8)2+(y–8)2=361 D) (x–8)2+(y+8)2=361
8) r=7;(h,k)=(0,–9)
A) x2+(y+9)2=7B)x
2+(y–9)2=7C)(x+9)2+y2=49 D) (x–9)2+y2=49
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
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–4)2+(y–2)2=64
A) (h,k)=(4
,
2);r=8 B) (h,k)=(4
,
2);r=64
C) (h,k)=(2
,
4);r=8 D) (h,k)=(2
,
4);r=64
14) (x–3)2+y2=100
A) (h,k)=(3
,
0);r=10 B) (h,k)=(0,3);r=10
C) (h,k)=(0,3);r=100 D) (h,k)=(3
,
0);r=100
Page63
15) x2+(y+2)2=4
A) (h,k)=(0,–2);r=2 B) (h,k)=(–2
,
0);r=2
C) (h,k)=(–2
,
0);r=4 D) (h,k)=(0,–2);r=4
16) 2(x+6)2+2(y+3)2=18
A) (h,k)=(–6
,
–3);r=3 B) (h,k)=(–6
,
–3);r=6
C) (h,k)=(6
,
3);r=3 D) (h,k)=(6
,
3);r=6
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)=(0,2)
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
Page66
3) r=5;(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=3;(h,k)=(–1
,
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
Page68
Graphtheequation.
5) x2+y2=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
Page69
6) (x–4)2+(y+3)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
Page70
7) x2+(y–1)2=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
Page71
8) (x–4)2+y2=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
Page72
3 WorkwiththeGeneralFormoftheEquationofaCircle
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Findthecenter(h,k)andradiusrofthecircle.Graphthecircle.
1) x2+y2–2x–12y+28=0
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) (h,k)=(1
,
6);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)=(–1
,
–6);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)=(1
,
–6);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)=(–1
,
6);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+6x+12y+36=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
,
–6);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
,
–6);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
,
6);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
,
6);r=3
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+18x+81+(y–6)2=64
A) (h,k)=(–9
,
6);r=8 B) (h,k)=(6
,
–9);r=8
C) (h,k)=(9
,
–6);r=64 D) (h,k)=(–6
,
9);r=64
4) x2–14x+49+y2–6y+9=64
A) (h,k)=(7
,
3);r=8 B) (h,k)=(3
,
7);r=8
C) (h,k)=(–7
,
–3);r=64 D) (h,k)=(–3
,
–7);r=64
5) x2+y2+12x–18y+117=36
A) (h,k)=(–6
,
9);r=6 B) (h,k)=(9
,
–6);r=6
C) (h,k)=(6
,
–9);r=36 D) (h,k)=(–9
,
6);r=36
Page74
6) x2+y2–10x+8y=40
A) (h,k)=(5
,
–4);r=9 B) (h,k)=(–4
,
5);r=9
C) (h,k)=(–5
,
4);r=81 D) (h,k)=(4
,
–5);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(7
,
9);tangenttox–axis
A) x2+y2–14x–18y+49=0B)x
2+y2–14x–18y+81=0
C) x2+y2+14x+18y+49=0D)x
2+y2–14x–18y+211=0
Solvetheproblem.
11) Ifacircleofradius5ismadetorollalongthex–axis,whatistheequationforthepathofthecenterofthe
circle?
A) y=5B)y=0C)y=10 D) x=5
12) Earthisrepresentedonamapofthesolarsystemsothatitssurfaceisacirclewiththeequatio
n
x2+y2+10x+2y–4070=0.Aweathersatellitecircles0.8unitsabovetheEarthwiththecenterofits
circularorbitatthecenteroftheEarth.Findthegeneralformoftheequationfortheorbitofthesatelliteon
thismap.
A) x2+y2+10x+2y–4173.04=0B)x
2+y2+10x+2y–37.36=0
C) x2+y2–10x–2y–4173.04=0D)x
2+y2+10x+2y+25.36=0
13) Findanequationofthelinecontainingthecentersofthetwocircles
x2+y2–8x–2y+16=0 and
x2+y2+2x–8y+13=0
A) –3x–5y+17=0B)5x–3y+17 =0C)
–3x+5y+17 =0D)3x–5y+17 =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) Ifasatelliteisplacedinacircularorbitof450 kilometersabovetheEarth,whatistheequationofthepath
ofthesatelliteiftheoriginisplacedatthecenteroftheEarth(thediameteroftheEarthisapproximately
12,740kilometers)?
A) x2+y2=46,512,400 B) x2+y2=202,500
C) x2+y2=40,576,900 D) x2+y2=173,976,100
16) Apoweroutageaffectedallhomesandbusinesseswithina10 miradiusofthepowerstation.Ifthepower
stationislocated11minorthofthecenteroftown,findanequationofthecircleconsistingofthefurthest
pointsfromthestationaffectedbythepoweroutage.
A) x2+(y–11)2=100 B) x2+(y+11)2=100
C) x2+(y–11)2=10 D) x2+y2=100
17) Apoweroutageaffectedallhomesandbusinesseswithina3 miradiusofthepowerstation.Ifthepower
stationislocated4miwestand4minorthofthecenteroftown,findanequationofthecircleconsistingof
thefurthestpointsfromthestationaffectedbythepoweroutage.
A) (x+4)2+(y–4)2=9B)(x–4)2+(y–4)2=9
C) (x+4)2+(y+4)2=9D)(x–4)2+(y+4)2=9
18) AFerriswheelhasadiameterof280feetandthebottomoftheFerriswheelis9feetabovetheground.
Findtheequationofthewheeliftheoriginisplacedonthegrounddirectlybelowthecenterofthewheel,
asillustrated.
280ft.
9ft.
A) x2+(y–149)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=10whent=4
A) v=5
2tB)v=2
5tC)v=10
4t D) v=4
10t
Page76
2) Avariesdirectlywitht2;A=12whent=2
A) A=3t2B) A=6t2C) A=3
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=18whenx=4
A) y=9
2xB)y=2
9xC)y=x+14 D) y=2x
6) y=5whenx=1
7
A) y=35x B) y=1
35xC)y=x+34
7D) y=1
5x
7) y=1.6whenx=0.8
A) y=2x B) y=0.8x C) y=x+0.8 D) y=0.5x
8) y=0.4whenx=1.6
A) y=0.25x B) y=0.4x C) y=x–1.2 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.IfPis2sec.whenLis16in.,whatistheperiodwhenthelengthis4in.?
A) 1sec B) 2sec C) 4 sec D) 8sec
12) Theamountofwaterusedtotakeashowerisdirectlyproportionaltotheamountoftimethattheshower
isinuse.Ashowerlasting22minutesrequires8.8gallonsofwater.Findtheamountofwaterusedina
showerlasting4minutes.
A) 1.6gal B) 48.4 gal C) 10 gal D) 2.2gal
Page77
13) Iftheresistanceinanelectricalcircuitisheldconstant,theamountofcurrentflowingthroughthecircuiti
s
directlyproportionaltotheamountofvoltageappliedtothecircuit.When7voltsareappliedtoacircuit,
70milliamperes(mA)ofcurrentflowthroughthecircuit.Findthenewcurrentifthevoltageisincreased
to11volts.
A) 110mA B) 77mA C) 99 mA D) 120 mA
14) Theamountofgasthatahelicopterusesisdirectlyproportionaltothenumberofhoursspentflying.The
helicopterfliesfor3hoursanduses21gallonsoffuel.Findthenumberofgallonsoffuelthatthe
helicopterusestoflyfor5hours.
A) 35gal B) 15gal C) 40 gal D) 42gal
15) Thedistancethatanobjectfallswhenitisdroppedisdirectlyproportionaltothesquareoftheamounto
f
timesinceitwasdropped.Anobjectfalls39.2metersin2seconds.Findthedistancetheobjectfallsin5
seconds.
A) 245mB)49mC)98mD)10m
2 ConstructaModelUsingInverseVariation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writeageneralformulatodescribethevariation.
1) Avariesinverselywithx2;A=4whenx=2
A) A=16
x2B) A=8
x2C) A=1x2D) A=8x2
Writeanequationthatexpressestherelationship.Usekastheconstantofvariation.
2) rvariesinverselyast.
A) r=k
tB) r=t
kC) r =kt D) kr=t
3) wvariesinverselyasthesquareofz.
A) w=k
z2B) w=z2
kC) w=k
zD) w=z
k
Ifyvariesinverselyasx,writeageneralformulatodescribethevariation.
4) y=8whenx=6
A) y=48
xB) y=4
3xC)y=x
48 D) y=1
48x
5) y=60whenx=7
A) y=420
xB) y=60
7xC)y=x
420 D) y=1
420x
6) y=12whenx=1
4
A) y=3
xB) y=48x C) y=x
3D) y=1
3x
Page78
7) y=1
5
whenx=25
A) y=5
xB) y=1
125 xC)y=x
5D) y=1
5x
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=72whenv=4.Findxwhenv=32.
A) x=9B)x=16 C) x=36 D) x=8
10) xvariesinverselyasy2,andx=4wheny=15.Findxwheny=5.
A) x=36 B) x=48 C) x=100 D) x=3
11) Whenthetemperaturestaysthesame,thevolumeofagasisinverselyproportionaltothepressureofthe
gas.Ifaballoonisfilledwith180cubicinchesofagasatapressureof14poundspersquareinch,findthe
newpressureofthegasifthevolumeisdecreasedto36cubicinches.
A) 70psi B) 18
7
psi C) 56 psi D) 65psi
12) Theamountoftimeittakesaswimmertoswimaraceisinverselyproportionaltotheaveragespeedofthe
swimmer.Aswimmerfinishesaracein30secondswithanaveragespeedof5feetpersecond.Findthe
averagespeedoftheswimmerifittakes50secondstofinishtherace.
A) 3ft/sec B) 4ft/sec C) 5 ft/sec D) 2ft/sec
13) Iftheforceactingonanobjectstaysthesame,thentheaccelerationoftheobjectisinverselyproportional
toitsmass.Ifanobjectwithamassof35kilogramsacceleratesatarateof3meterspersecondpersecond
(m/sec2)byaforce,findtherateofaccelerationofanobjectwithamassof7kilogramsthatispulledby
thesameforce.
A) 15m/sec2B) 3
5
m/sec2C) 12m/sec2D) 10m/sec2
14) Ifthevoltage,V,inanelectriccircuitisheldconstant,thecurrent,I,isinverselyproportionaltothe
resistance,R.Ifthecurrentis240milliamperes(mA)whentheresistanceis2ohms,findthecurrentwhen
theresistanceis12ohms.
A) 40mA B) 1440 mA C) 1434 mA D) 80mA
15) Whiletravelingataconstantspeedinacar,thecentrifugalaccelerationpassengersfeelwhilethecari
s
turningisinverselyproportionaltotheradiusoftheturn.Ifthepassengersfeelanaccelerationof12feet
persecondpersecond(ft/sec2)whentheradiusoftheturnis70feet,findtheaccelerationthepassengers
feelwhentheradiusoftheturnis280feet.
A) 3ft/sec2B) 4ft/sec2C) 5ft/sec2D) 6ft/sec2
Page79
3 ConstructaModelUsingJointVariationorCombinedVariation
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writeageneralformulatodescribethevariation.
1) ThesquareofGvariesdirectlywiththecubeofxandinverselywiththesquareofy;G=2whenx=4 and
y=3
A) G2=9
16
x3
y2B) G2=3
2
x3
y2
C) G2=256
9
y3
x2D) G2=1
144
(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=75 whenx=125 andy=3.
A) z=5
3
3xy2B) z=3
5
3xy2C) z=135
3x
y2D) z=1
135
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=319.2in3whenT=570°andP=25lb/in2.Whatisthevolume
onthisdevicewhenthetemperatureis160°andthepressureis20lb/in2?
A) V=112in3B) V=8in3C) V=132in3D) V=92in3
8) Thetimeinhoursittakesasatellitetocompleteanorbitaroundtheearthvariesdirectlyastheradiuso
f
theorbit(fromthecenteroftheearth)andinverselyastheorbitalvelocity.Ifasatellitecompletesanorbit
840milesabovetheearthin9hoursatavelocityof25,000mph,howlongwouldittakeasatelliteto
completeanorbitifitisat1600milesabovetheearthatavelocityof24,000mph?(Use3960milesasthe
radiusoftheearth.)
A) 10.86hr B) 17.86 hr C) 3.13 hr D) 108.59 hr
Page80
9) Thepressureofagasvariesjointlyastheamountofthegas(measuredinmoles)andthetemperatureand
inverselyasthevolumeofthegas.Ifthepressureis1131kiloPascals(kPa)whenthenumberofmolesis8,
thetemperatureis290°Kelvin,andthevolumeis960cc,findthepressurewhenthenumberofmolesis6,
thetemperatureis330°K,andthevolumeis720cc.
A) 1287kPa B) 1248 kPa C) 2574 kPa D) 2652 kPa
10) Body–massindex,orBMI,takesbothweightandheightintoaccountwhenassessingwhetheran
individualisunderweightoroverweight.BMIvariesdirectlyasoneʹsweight,inpounds,andinverselyas
thesquareofoneʹsheight,ininches.Inadults,normalvaluesfortheBMIarebetween20and25.Aperson
whoweighs161poundsandis67inchestallhasaBMIof25.21.WhatistheBMI,tothenearesttenth,fora
personwhoweighs128poundsandwhois66inchestall?
A) 20.7 B) 21 C) 20.3 D) 20
11) Theamountofpaintneededtocoverthewallsofaroomvariesjointlyastheperimeteroftheroomand
theheightofthewall.Ifaroomwithaperimeterof40feetand10–footwallsrequires4quartsofpaint,
findtheamountofpaintneededtocoverthewallsofaroomwithaperimeterof70feetand6–footwalls.
A) 4.2qt B) 420qt C) 42 qt D) 8.4qt
12) Thepowerthataresistormustdissipateisjointlyproportionaltothesquareofthecurrentflowing
throughtheresistorandtheresistanceoftheresistor.Ifaresistorneedstodissipate27wattsofpower
when3amperesofcurrentisflowingthroughtheresistorwhoseresistanceis3ohms,findthepowerthat
aresistorneedstodissipatewhen4amperesofcurrentareflowingthrougharesistorwhoseresistanceis
6ohms.
A) 96watts B) 24watts C) 144 watts D) 72watts
13) Whiletravelinginacar,thecentrifugalforceapassengerexperiencesasthecardrivesinacirclevarie
s
jointlyasthemassofthepassengerandthesquareofthespeedofthecar.Ifapassengerexperiencesa
forceof403.2newtons(N)whenthecarismovingataspeedof80kilometersperhourandthepassenger
hasamassof70kilograms,findtheforceapassengerexperienceswhenthecarismovingat20kilometers
perhourandthepassengerhasamassof50kilograms.
A) 18NB)20NC)16ND)24N
14) Theamountofsimpleinterestearnedonaninvestmentoverafixedamountoftimeisjointlyproportional
totheprincipleinvestedandtheinterestrate.Aprincipleinvestmentof$4800.00withaninterestrateof
5%earned$480.00insimpleinterest.Findtheamountofsimpleinterestearnediftheprincipleis$4700.00
andtheinterestrateis1%.
A) $94.00 B) $9400.00 C) $470.00 D) $96.00
15) Thevoltageacrossaresistorisjointlyproportionaltotheresistanceoftheresistorandthecurrentflowin
g
throughtheresistor.Ifthevoltageacrossaresistoris15volts(V)foraresistorwhoseresistanceis5ohms
andwhenthecurrentflowingthroughtheresistoris3amperes,findthevoltageacrossaresistorwhose
resistanceis6ohmsandwhenthecurrentflowingthroughtheresistoris4amperes.
A) 24VB)20VC)12VD)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
Page83
5 KnowHowtoGraphKeyEquations
2.3 Lines
1 CalculateandInterprettheSlopeofaLine
2 GraphLinesGivenaPointandtheSlope
3 FindtheEquationofaVerticalLine
4 UsethePoint–SlopeFormofaLine;IdentifyHorizontalLines
Page84
5 FindtheEquationofaLineGivenTwoPoints
6 WritetheEquationofaLineinSlope–InterceptForm
7 IdentifytheSlopeandy–InterceptofaLinefromItsEquation
8 GraphLinesWritteninGeneralFormUsingIntercepts
9 FindEquationsofParallelLines
10 FindEquationsofPerpendicularLines
2.4 Circles
1 WritetheStandardFormoftheEquationofaCircle
2 GraphaCircle
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3 WorkwiththeGeneralFormoftheEquationofaCircle
2.5 Variation
1 ConstructaModelUsingDirectVariation
2 ConstructaModelUsingInverseVariation
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3 ConstructaModelUsingJointVariationorCombinedVariation
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