5 Graphing linear equations.docx
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5Graphinglinearequations
Graphinglinearequations
1.Theaveragepriceofacertaintypeofcoffeeworldwidewas$0.51perpoundin2008.Thepriceperpoundincreasedabout$0.18eachyearuntil2014,andisexpectedtodosoforthenexttwoyears.Whichofthefollowinggraphsrepresentstherelationshipbetweenyearsafter2008,t,andpriceperpound,P,indollars,ofthiscoffeeworldwide?
A.
B.
C.
D.
CorrectAnswer:
ADifficultlevel:
3
2.AfarmerobservesthatthedemandforcornQ,inthousandsofbushelspermonth,andpriceP,indollarsperbushel,arerelatedbyalinearfunction.Ifademandof2,500bushelspermonthcorrespondstoapriceof$4.00perbushel,andademandof3,000bushelspermonthcorrespondstoapriceof$3.20perbushel,whichofthefollowinggraphsrepresentstherelationshipbetweenPandQ?
A.
B.
C.
D.
CorrectAnswer:
DDifficultlevel:
3
3.ThelinesfandgaregraphedBELOWinthexy-plane.Linegcanbewrittenastheequationy=ax+b,whereaandbareconstants.Whichofthefollowingequationsrepresentslinef?
Pleasechoosefromoneofthefollowingoptions.
A.y=ax−b
B.y=−ax+b
C.−y=ax+b
D.x=ay+b
CorrectAnswer:
CDifficultlevel:
3
4.Whichofthefollowinggraphsrepresentstheequation（y+6）=
A.
B.
C.
D.
CorrectAnswer:
ADifficultlevel:
3
5.Theequation6y+12x=18isgraphedinthexy-plane.Whichofthefollowingequationshasagraphthatisperpendiculartothegraphoftheaboveequation?
A.y=-2x+3
B.y=
x+3
C.y=2x+3
D.y=-
x+3
CorrectAnswer:
BDifficultlevel:
3
6.Whichofthefollowingequationsrepresentsalineinthexy-planewithanx-interceptat（-2,0）andaslopeof4?
A.y=4x+8
B.y=-4x+8
C.y=4x-2
D.y=-4x-2
CorrectAnswer:
ADifficultlevel:
2
7.Theequationy=
（x−8）isgraphedinthexy-plane.Whichofthefollowingequationswillhaveagraphthatisparalleltothegraphoftheaboveequationandhaveanx-interceptonthenegativex-axis?
A.y=
（x+8）
B.y=
x-8
C.y=
x+8）
D.y=
x-8
CorrectAnswer:
ADifficultlevel:
2
8.Theequationy=x+aisgraphedinthexy-plane,whereaisapositiveconstant.Asecondequation,y=x-a,isgraphedinthesamexy-plane.Howdotheslopeandy-interceptofthegraphofthefirstequationcomparewiththeslopeandy-interceptofthegraphofthesecondequation?
A.Theslopesarethesame;they-interceptofthefirstequation'sgraphisthepoint（0,a）,andthey-interceptofthesecondequation'sgraphisthepoint（0,−a）.
B.Theslopesarethesame;they-interceptofthefirstequation'sgraphisthepoint（0,-a）,andthey-interceptofthesecondequation'sgraphisthepoint（0,a）.
C.They-interceptsarethesame;theslopeofthefirstequation'sgraphisa,andtheslopeofthesecondequation'sgraphis-a.
D.They-interceptsarethesame;theslopeofthefirstequation'sgraphis−a,andtheslopeofthesecondequation'sgraphisa.
CorrectAnswer:
ADifficultlevel:
2
9.WhichofthefollowingisanequationofthelineAgraphedinthexy-planethatpassesthroughthepoint（−1,3.5）andisperpendiculartothelineBwhoseequationisx+4.5=0?
A.x=-1
B.x=3.5
C.y=3.5
D.y=4.5
CorrectAnswer:
CDifficultlevel:
2
10.AlineisgraphedasshownBELOW.Whichofthefollowingequationsrepresentstheline?
A.y=
x+2
B.y=
x-2
C.y=
x+2
D.y=
x-2
CorrectAnswer:
DDifficultlevel:
2
11.WhichofthefollowingequationsrepresentsthelinegraphedBELOWinthexy-plane?
A.x=-4
B.y=-4
C.y=x-4
D.x=y-4
CorrectAnswer:
BDifficultlevel:
2
12.Whichofthefollowingequationsrepresentsalineinthexy-planewithanx-interceptat（−2,0）andaslopeof4?
A.y=4x+8
B.y=-4x+8
C.y=4x-2
D.y=-4-2
CorrectAnswer:
ADifficultlevel:
2
13.Whichofthefollowingequationsrepresentsalineinthexy-planewithanx-interceptat（−15,0）anday-interceptat（0,−9）?
A.
B.
C.
D.
CorrectAnswer:
BDifficultlevel:
3
14.Twolinesgraphedinthexy-planehavetheequations2x+5y=20andy=kx-3,wherekisaconstant.Forwhatvalueofkwillthetwolinesbeperpendicular?
A.
B.
C.
D.
CorrectAnswer:
CDifficultlevel:
3
15.Arectangleissaidtohaveagoldenratioiftheratioofitslengthtowidthisequaltoapproximately1.6.Whichofthefollowinggraphsrepresentstherelationshipbetweenlength,l,andwidth,w,inagoldenrectangle?
A.
B.
C.
D.
CorrectAnswer:
ADifficultlevel:
3
16.ThelinegraphedBELOWinthexy-planecanbewrittenastheequationy-c=m（x-d）,wherec,d,andmareconstants.Whichofthefollowingrepresentsthegraphofy-c+4=m（x-d-4）?
A.
B.
C.
D.
CorrectAnswer:
ADifficultlevel:
3
17.Whichofthefollowingrepresentsthegraphoftheequation3y-7=0?
A.
B.
C.
D.
CorrectAnswer:
CDifficultlevel:
4
18.Theequationsx+y=3and-5x-5y=-15aregraphedinthexy-plane.Whichofthefollowingmustbetrueofthegraphsofthetwoequations?
A.Theslopeofthegraphofx+y=3is11andtheslopeofthegraphof-5x-5y=-15is−1.
B.Thegraphsofthetwoequationsareperpendicularlines.
C.Theyy-interceptofthegraphof-5x-5y=-15−5x−5y=−15is-15−15.
D.Thegraphsofthetwoequationsarethesameline.
CorrectAnswer:
DDifficultlevel:
4
19.Whichofthefollowingrepresentsthegraphoftheequationx=
A.
B.
D.
C.
CorrectAnswer:
DDifficultlevel:
4
20.Thelinerepresentedbytheequationy=
isgraphedinthexy-plane.Whichofthefollowingstatementscorrectlydescribesthegraphoftheline?
A.Thelineisperpendiculartothegraphx+y=1.
B.Thelinehasanegativeslopeandapositivey-intercept.
C.Thelinehasapositiveslopeandanegativey-intercept.
D.Thex-interceptisequaltothenegativeofthey-intercept.
CorrectAnswer:
BDifficultlevel:
4
21.Ifkisarationalconstantnotequalto1,whichofthefollowinggraphsrepresentstheequationy+5=k（x+y）+5?
A.
B.
C.
D.
CorrectAnswer:
ADifficultlevel:
4
22.Whatistheequationofthelinegraphedinthexy-planethatpassesthroughthepoint（-4,-5）andisparalleltothelinewhoseequationis3x-4y=-8?
A.
B.
C.
D.
CorrectAnswer:
BDifficultlevel:
4
23.Theequationsbelowaregraphedinthexy-plane.Whichequation'sgraphwillhaveaslopeof
anday-interceptof3?
A.7x+8y=24
B.7x-8y=-24
C.8x+7y=3
D.7x-8y=3
CorrectAnswer:
BDifficultlevel:
4
24.TheequationforthegravitationalpotentialenergyUofa1-kilogramobjectonEarthrestinghmetersabovethegroundtsecondsafterplacementisU=9.8hjoules.WhichofthefollowingisagraphofUversustfora1-kilogramobject2metersabovetheground?
A.
B.
C.
D.
CorrectAnswer:
CDifficultlevel:
4
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