Geometry Chapter 3 Notes - Canyon Crest Academy ?· Geometry Chapter 3 Notes Notes #13: Section 3.1 and Algebra Review A ... A. Parallel and Perpendicular Lines ...

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1 GeometryChapter3NotesNotes#13:Section3.1andAlgebraReviewA.Definitions:ParallelLines:Draw:Example:Transversal: alinethatintersectstwoormorecoplanarlinesindifferentpointsDraw:Example:ParallelPlanes:Draw:Example:Practice:1.) NameaplaneparalleltoABGH.2.) NamethreelinesparalleltoCFsuur3.) Classifytheplanesasintersectingorparallel:ADEHandBCFG4.) Drawandlabelthefiguredescribed: ABsuurand XYsuurarecoplanarandparallel. hisatransversalthatintersectsthematpointsCandZ,respectively.B.SpecialAngles:Theanglesformedbylinesandtheirtransversalsarespecial:AlternateInteriorAngles: ( ) SamesideInteriorAngles:( )2 CorrespondingAngles:( ) AlternateExteriorAngles: ()SamesideExteriorAngles:( )VerticalAngles: (reminder)( )Practice: Classifyeachpairofanglesasalt.int.,ssint.,corr,alt.ext.,ssext,orvertical.5.) 1, 5 6.) 2, 8 7.) 4, 2 8.) 3, 8 9.) 1, 7 10.) 4, 7 8 7654 321C.IdentifyingLinesandTransversals: Namethetwolinesandthetransversalthatformeachpairofangles.Whattypeofspecialanglesarethey?(Hint: Tracetheanglesintwodifferentcolorswherethey overlapisthetransversal,theleftoversarethetwolines.)11.) 4, 2 lines:____,_____transversal:______type:_______________12.) ,B BAD lines:____,_____transversal:______type:_______________13.) , 5BAD lines:____,_____transversal:______type:_______________54321BACD E14.) , 5BCD lines:____,_____transversal:______type:_______________3 D.AlgebraPractice: SolvingLinearSystemsbyAddition/Subtraction/EliminationRearrangeeachequationsothatthevariableexpressionsareontheleftsideoftheequalssignandtheconstantisontherightsideoftheequalsign(calledStandardForm)Multiplywholeequationssothatonevariableexpressionisequalbuthastheoppositesign.AddtheequationstogetherwatchonevariablecanceloutSolveforBOTHvariablesWriteyouranswerasapoint(x, y) (inalphabeticalorder)15.)2x 3y=8 16.) x =4y 34x+3y=2 3x 2y=517.) 3x 5y=11 18.) 2x+3y 10=x+y 142x 4y=9 x 2y+5=2x y+6Solveforxandy:19.)2xy703x35x154 Notes#14:Sections3.1and3.2A.RelationshipsformedbyparallellinesAlternateInteriorAnglesTheoremIftwo________________linesarecutbya__________,thenalternateinterioranglesare_________________.(Itsconverse):Iftwolinescutbya________________formcongruentalternateinteriorangles,thenthelinesare________________.CorrespondingAnglesPostulateIftwo________________linesarecutbya__________,thencorrespondinganglesare_________________.(Itsconverse):Iftwolinescutbya________________formcongruentcorrespondingangles,thenthelinesare________________.SameSideInteriorAnglesTheoremIftwo________________linesarecutbya__________,thensamesideinterioranglesare_________________.(Itsconverse):Iftwolinescutbya________________formsupplementarysamesideinteriorangles,thenthelinesare________________.AlternateExteriorAnglesTheoremIftwo________________linesarecutbya__________,thenalternateexterioranglesare_________________.(Itsconverse):Iftwolinescutbya________________formcongruentalternateexteriorangles,thenthelinesare________________.SameSideExteriorAnglesTheoremIftwo________________linesarecutbya__________,thensamesideexterioranglesare_________________.(Itsconverse):Iftwolinescutbya________________formsupplementarysamesideexteriorangles,thenthelinesare________________.5 Completethesentencesandsolveforx.1.) Thelabeledanglesare____________anglesandtheirmeasuresare___________becauseofthe_________________________________________3x+101002.)Thelabeledanglesare____________anglesandtheirmeasuresare______________________becauseofthe_____________________________1203x3.)Thelabeledanglesare____________anglesandtheirmeasuresare___________________becauseofthe_____________________________2x+524x84.)Thelabeledanglesare____________anglesandtheirmeasuresare___________________becauseofthe_____________________________2x+217x4B.IdentifyingParallelLines: Usethegiveninformationtonamethelinesthatmustbeparallel.(Traceanglesandlookforspecialpairsofanglesandspecialrelationships.)10987654321WS TUV5.) 1 4 Typeofanglepair: Relationship:Parallellines?:6.) 1 2 3 180m m m + + = oTypeofanglepair: Relationship:Parallellines?:7.) 9 2 Typeofanglepair: Relationship:Parallellines?:8.) 4 7 Typeofanglepair: Relationship:Parallellines?:9.) 2 10 Typeofanglepair: Relationship:Parallellines?:6 C.SpecialPairsofAnglesSolveforallvariables.Allmeasurementsareindegrees.(Hint:extendtheparallellinesandlookforspecialpairsofangles)10.)120xy11.)4x120802y12.)edcba27605613.)1302x5y2x3y110D.ProofswithParallelLines:14.)Provethealternateexterioranglestheorem:Ifatransversalintersectstwoparallellines,thenalternateexterioranglesarecongruent.Given: k lPProve: 1 3 lk321Statements Reasons1.)2.)3.) 3 ____ 4.)1.)2.)CorrespondingAnglePostulate3.)4.)7 15.) Provetheconverseofthealternateexterioranglestheorem:Iftwolinesandatransversalformalternateexterioranglesthatarecongruent,thenthetwolinesareparallel.Given: 1 3 Prove: m nPnm321Statements Reasons1.)2.) 1 _____ 3.)4.)1.)2.)3.) Substitution4.) Iftwolinesandatransversalform______________________________angles,thenthetwolinesare________________.Notes#15:Sections3.3and3.4A.ParallelandPerpendicularLinesProvetheconverseofthesamesideinterioranglestheorem:Iftwolinesandatransversalformsamesideinterioranglesthataresupplementary,thenthetwolinesareparallel.Given: 2 and 3 aresupplementaryProve: m nPnm321Statements Reasons1.)2.) 2 3 _____m m + =3.) 2 ____ _____m m + =4.)5.) 2 2m m = 6.)7.)1.)2.) Definitionof__________________angles3.)4.) Substitution5.)6.)Subtraction7.)Iftwolinesandatransversalform______________________________angles,thenthetwolinesare________________.8 Iftwolinesareparalleltothesameline,thentheyare___________toeachother.Inaplane,iftwolinesareperpendiculartothesameline,thentheyare_____________toeachother.Inaplane,ifalineisperpendiculartooneoftwoparallellines,thenitisalso_____________totheother.Examples:For#13,considercoplanarlinesj,k,l,andm. Given eachof thefollowingstatements,whatmore,ifanything,canyouconcludeaboutthelines?1.) ,j k k mP P 2.) ,j k l k P 3.) , ,j k k l l m PB.ClassifyingTriangles Trianglesaredescribedbasedon thelengthsof theirsidesandthemeasuresoftheiranglesSidesScalene Isosceles Equilateral9 AnglesAcute Obtuse RightEquiangularExamples: For#57,classifyeachtriangle(drawntoscale)byitsanglesandsides.5.) 6.) 7.)For#810,drawatriangle,ifpossible,tofiteachdescription.8.)obtusescalene 9.)acuteisosceles 10.)rightequilateral11.)Theperimeterof ABCis32m.AB=4x2,BC=3x+1,AC=2x+6.Writean equationandsolveforx.Then,classifythetriangleasscalene,isosceles,orequilateral.(Hint:drawapicturefirstandlabelwhatyouknow)C.Theanglesofatriangle:**Thesumoftheinterioranglesofatriangleisalways______**10 13.)Findthemissingvaluesandclassify LMNV :12.)3211 2 3 _____m m m + + =x4x+112x+8ML NLMNV is__________and __________________________xm Lm Mm N = = = =14.)Findthevaluesofeachvariableandthemeasureofeachangle.Thenclassifyeachtrianglebyitsangles.(Allmeasurementsshownareindegrees)13461w xyzDCBA________________wxyz = = = =is_________is_________is_________ABCABDDBCV V V**Themeasureofanexteriorangleofatriangleequalsthesumofthemeasuresofthetwo_________________ __________________angles.**Explore:85401234567Diagramfor#1515.)Complete:1 2 _____2 7 _____7 3 _____4 3 5 6 _____2 3 7 _____m mm mm mm m m mm m m + = + = + = + + + = + + =11 16.)Solveforxandy:y9550x17.) 2 103 , 3 156 , 1 _____m m m = = = o o321Notes#16:Section 3.5andAlgebraReviewA. Polygons:(_________sidedfigures)ConvexPolygon ConcavePolygonExplore:Triangle ____sidesSumofInteriorAngles=______SumofExteriorAngles=______Quadrilateral____sidesSumofInteriorAngles=______SumofExteriorAngles=______Pentagon ____sidesSumofInteriorAngles=______SumofExteriorAngles=______Hexagon ____sidesSumofInteriorAngles=______SumofExteriorAngles=______OtherCommonPolygons:Octagon:______sidesNonagon:______sidesDecagon:________sidesDodecagon:________sides18gon:______sides20gon:______sidesngon:______sides12 Patternsfor polygonalanglesums:SumofInteriorAngles SumofExteriorAngleseachinteriorangle+eachexteriorangle=___________Findthesumofthemeasuresoftheanglesofeachpolygon:(interiorangles)1.) decagon 2.) octagon 3.)22gonFindthemissinganglemeasures:(allmeasuresshownareindegrees)4.)130a114285.)b 13110716012385B. RegularPolygons (wherenisthenumberofsidesinthepolygon)RegularPolygons: allsides________________allangles________________InteriorAnglesSumofInteriorAngles:OREachInteriorAngle:ExteriorAnglesSumofExteriorAngles:EachExteriorAngle:ExtraTrick:(eachinteriorangle)+(eachexteriorangle)=________13 Completethechartusingtheserelationships.(Picturesmayhelp!)6. 7. 8. 9. 10. 11.#ofsides(n) 6 8SumofExteriorAnglesEachExteriorAngle 72EachInteriorAngle 90SumofInteriorAngles 900 28806.) 7.) 8.)9.) 10.) 11.)D.WordProblems:Definetwovariablesandwritetwoequationstosolve.12.)Thesumoftwonumbersis18andtheirdifferenceis6.Findeachofthenumbers.13.)Thesumoftwonumbersisonemorethantwicethesmallernumber.Theirdifferenceissevenlessthantwicethelargernumber.Findthenumbers.14 D.AlgebraPractice: Solvinglinearsystemswithfractionsand/ordecimals.Tocleardecimals: multiplybothsidesoftheequationbyamultipleof10scootthedecimaloverToclearfractions: multiplybothsidesoftheequationbythecommondenominatorcrosscancel14.)0.2 0.5 1.41 1 12 3 3m nm n = + = 15.)0.2 1.2 8.81 1 14 6 6m nm n + = =Notes#17:Section 3.6A.Slope:Slopeisusedtodescribethe________________and_________________oflines.Sketchalinewith:a)positiveslope b)negativeslope c)zeroslope d)undefinedslope15 Alineisshown.Usetwomarkedpointsandcountriseoverruntofindtheslopeoftheline.1.) 2.) 3.)Slope= Slope= Slope=Withoutusingagraph andgiventwopoints: ( )1 1,x y and ( )2 2,x ySlope= m=2 12 1y yx x 0 00nn undefined = =For#45,findtheslopeofthelinepassingthrough thetwogiven points:4.)(4,1),(3,2) 5.)(6, 3)and(2,1)6.)Alinewithslope73passesthroughthepoints(1,2)and(2, y).Findy.B.GraphingLinesTherearemanywaystographaline.Youneedtoknowhowtographaline:(i)givenapointandaslope,(ii)by findingthexinterceptandyintercept,and(iii) by findingtheyinterceptandtheslopeoftheline.16 (i)GraphinglinesusingapointandaslopeApointPonalineandtheslopeofthelinearegiven.Sketchthelineandfindthecoordinatesoftwootherpointsontheline7.) 8.) 9.)P(2,1)slope= 451stpoint:2ndpoint:P(0,3)slope=21stpoint:2ndpoint:P(2,0)slope=231stpoint:2ndpoint:(ii).GraphingLinesusingthexandy intercepts.Theinterceptsarethepoint(s)wherealineintersectstheaxesofthecoordinateplane.Findthexandyintercepts(bysettingtheoppositevariabletozero)WritetheseanswersastwodifferentpointsGraphandconnectthesepointstographthelineLabelthegraphedlinewiththeoriginalequationMostcommonerror: Forgettingthattheinterceptsaretwodifferentpointsandgraphingasjustone10.)x+2y=4xintercept yintercept(sety=0)(setx=0)xint:(,0)yint:(0, )11.)3x y=3xint:(,)yint:(,)10 987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y17 (iii) GraphingLinesusingtheslopeandyintercept:Getyalonesotheequationisin y=mx+bform (m=_________,b=_________)Graph bfirst.Thispointgoesonthe____axis.Useslopeandcountriseoverrun tothenextpoint(s).Whenyouhaveatleastthreepoints, thenconnectthepointstomakealine.LabelyourgraphedlinewiththeoriginalequationMostcommonerrors: Graphingbonthexaxisinsteadoftheyaxis Graphingtheslopeinthewrongdirection(e.g.forgettinganegative)12.)1 52y x = ( Imalreadyinslopeinterceptform!)m=___(graphmesecond!Watchthenegative!)b= ___( graphmefirst!Igoontheyaxis!)13.)x 2y=2( Getmeinslopeinterceptform first)m=______b=______14.)x+3y=6( Getmeinslopeinterceptform first)m=______b=______10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910yGraphfor#13AND#14(besuretolabelyourlines!)18 SpecialCases:GraphingHorizontalandVerticalLines15.)x=4(ThisequationdescribesthelineforwhichALLpointshavean xcoordinateof4.Therearenorestrictionsonthevalueof y).16.)y=2(ThisequationdescribesthelineforwhichALLpointshavean ycoordinateof 2.Therearenorestrictionsonthevalueof x).17)x=1Usethepatternyoufoundabovetocompletethesesentences:Anylineintheform x=_____isa________________linebecauseitintersectsthe____________Anylineintheform y=_____isa________________linebecauseitintersectsthe____________Usethispatterntographtheselineswithoutatableofsolutions.18.)y=3 19.)x=2 20.)y=419 Notes#18:WritingLinearEquationsA.Convertingequationsoflines:LinescanbewrittenineitherSlopeInterceptform(y=mx+b)orStandardForm(Ax+By=C).Youneedtoknowhowtoconvertfromonetotheother.ConvertingtoSlopeInterceptFormGoal:y=mx+ b(wheremand bareintegersorfractions) Getyalone ReduceallfractionsConvertingtoStandardFormGoal: Ax+ By= C(whereA,B,andCareintegersandwhereAispositive) Getx andytermsontheleftsideandtheconstanttermontherightsideoftheequation MultiplyALLtermsbythecommondenominatortoeliminatethefractions Ifnecessary,changeALLsignssothatthexterm ispositive1.) Converttoslopeinterceptform:4x12y=82.) Converttostandardform:2 53y x = B. Writinglinearequationsgiventheslopeand yinterceptFindtheslope(m)andyintercept(b)[Ifthegiveninformationisagraph,thenyouwillhavetocountbyhandtofindthesevalues.]Fillinmandbsoyouhaveanequationofthelineiny=mx+bform.y=________x +____________( Putm here!) ( Putb here!)3.) Findtheequationofthelinewithslopeof5andyinterceptof 2.Writeinstandardform.4.) Findtheequationofthegivenlineinslopeinterceptform.5.) Writetheequationofalinethathasthesameslopeas 4 35y x = andhasayinterceptof1.Writeinstandardform.20 C. Writinglinearequationsgiven theslopeandapoint plugslope=mintoy=mx+b nameyourpoint(x,y)andplugthesevaluesinforxandy solveforb plugmandbbackintoy=mx+b converttostandardform,ifnecessary**Remembertoleavexandyasvariables!**6.)Findtheequationofthelinewithslopeof 2andgoingthrough(1,3)inslopeinterceptform.7.)Findtheequationofthelinewithslopeof 13andgoingthrough(6, 2)instandardform.8.) Findtheequationofthelineinslopeinterceptform withslope 25 andpassingthroughthepoint(3,7).D. Writinglinearequationsgiven twopoints findtheslope pickoneofyourpointstobexandy plugm,x,yintoy=mx+b solveforbplugmandbintoy=mx+b converttostandardform,ifnecessary**Remembertoleavexandyasvariables!**9.)Findtheequationofthelinegoingthrough(3,1)and(4,8)inslopeinterceptform.10.)Findtheequationofthelinewithxintercept3andyintercept2instandardform.11.) Findtheequationofthelinegoingthrough(5,2)and(1,3)in standardform.12.)Findtheequationofthelinewith xintercept5andyintercept4 in slopeinterceptform.21 Notes#19:Section3.7A.Review WritingLinearEquations:1.)Findtheequationofthelinewithslopeof34andgoingthrough(1,5)inslopeinterceptform.2.) Findtheequationofthelinegoingthrough(1,0)and(4,2)inslopeinterceptform.3.)Findtheequationofthelinewithxintercept1andyintercept2instandardform.4.)Findtheequationofthelinegoingthrough(4,3)withxintercept6in standardform.B.ParallelandPerpendicularLinesFor#56,apairof parallellinesandapairofperpendicularlinesaregraphedbelow.Usethegraphstofindtheslopeofeachofthefourlinesandtocompletethesentences.5.)10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910ySlopeof 1l :Slopeof 2l :Parallellineshave_________slopes.22 6.)10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910ySlopeof 3l :Slopeof 4l :Perpendicularlineshave____________,_____________slopes.Theslopeofalineisgiven.Findtheslopeof alineparalleltoitandtheslopeofalineperpendiculartoit:7.)m= 23 8.)m=7 9.) m=0Arethelineswiththeseslopesparallel,perpendicular,orneither?10.) 11.) 4,4 12.) 1,113.) Findtheslopeofalineparallelandperpendicularto ABsuurwhereA(3,1)andB(2,4),2 43 623 For#1416,statewhetherthegivenpairoflinesisparallel,perpendicular,orneither:14.)3 148 6 12y xx y = + =15.)1 522 4 9y xx y = + + =16.)5 45 4y xx y = + = +C. Writinglinearequationsgiven apointandanotherline(parallelorperpendiculartoyourline) findmfromthegivenline ifthelineisparallel,thisisyourmifthelineisperpendicular,findits_____________________________ plugm,x,yintoy=mx+b solveforbplugmandbintoy=mx+b converttostandardform,ifnecessary**Remembertoleavexandyasvariables!**17.)Findtheequationofthelinegoingthrough(1,2)andparalleltoy=3x+4inslopeinterceptform.18.)Findtheequationofthelinegoingthrough(3, 2)andperpendiculartox 4y=3instandardform.19.)Findtheequationofthelinegoingthrough(1,5)andperpendiculartoy=3x+4inslopeinterceptform.20.)Findtheequationofthelinegoingthrough(9, 3)andparallel to2x 3y=3instandardform.24 Notes#20:ReviewYoucannowsolvelinearsystems(asetof2lines)usingalgebra(substitution/elimination)ANDusingcoordinateGeometry(graphing).Youshouldgetthesameanswerforbothmethods.solvetheequationsusingsubstitutionoreliminationwriteyouranswerasapoint( , )graphthetwolinesusingeithertheinterceptmethodORslopeinterceptmethodconfirmthatthetwolinesintersect(meet)atyoursolutionpoint1.) y=x 2x+ y=41stMethod:substitutionoreliminationsolution:(,)2ndMethod:graphing(graphbothlinesonthecoordinateplanebelow)10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y2.) 2x y= 3x+ 2y=61stMethod:substitutionoreliminationsolution:(,)2ndMethod:graphing(graphbothlinesonthecoordinateplanebelow)10987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y25 Chapter3StudyGuideFor#14,identifywhethertheanglesareverticalangles,samesideinteriorangles,correspondingangles,alternateinteriorangles,samesideexteriorangles,oralternateexteriorangles.1.) 2and 6 3.) 5and 2 2.) 1and 6 4.) 4and 7 7654321For#56,findtheslopeofthelinepassingthroughthetwopoints5.)(3,2)and(4,1) 6.)(9,2)and(2,2) 7.)Theslopeof linelisgiven.Findtheslopeofthelineparalleltoitandtheslopeofthelineperpendiculartoit:a) 2b)3/2For#810,namethetwolinesandtransversalthatformeachpairofangles:8.) 1, 3 lines:____,____trans:______9.) ,BAD CDA lines:____,____trans:______10.) , 5BAD lines:____,____trans:______54321BACD EInthediagrams,thelinesshownareparallel.Writeanequationandsolvefor xandy.(Theanswerto#12istwofractions.)Justifyyourwork.2x+40x+805y+2011.)2x+102y+20y+6512.)Findthevaluesofxandy.13.)4020yx14.)5x15x205y26 Defineyourvariables,writeanequation,andsolve:15.) Thesumoftwonumbersis10.Thedifferenceofthefirstnumberandtwicethesecondnumberis1.Findthenumbers.Ineachexercise,someinformationisgiven.Usethisinformationtonamethesegmentsthatmustbeparallel.Iftherearenosuchsegments,writenone.16.) 3 10 18.) 2 3 17.) 7 10 19.) 9 5 1110987654321A BF CEDSolveforxandy:20.)6x2y140x+y130Solveforxandy:21.)1 1 12 42 1 83 2x yx y + = = 22.) Prove theconverseofthealtextanglestheorem:Iftwolinesandatransversalformalternateexterioranglesthatarecongruent,thenthetwolinesareparallel.Given: 1 3 Prove: m nPnm321Statements Reasons1.)2.)3.)4.)1.)2.)3.)4.)27 23.) Given: l mPProve: 2 4 180m m + = o4 321mlStatements Reasons1.)2.)3.)4.)1.)2.)3.)4.)For#2526,classifythetrianglesbasedontheirsidesandtheirangles:25.)23.)2x3x+ 58x2026.)24.)60 6024.) Given:AB=CDAE=FDProve:EB=CFA BC DEFStatements Reasons1.)2.)3.)4.)AE=FD5.)1.)2.)3.)4.)5.)28 Usethediagram forreference.Showallequationsandwork.27.)Ifm 6 42andm 8 61,thenm 10 ____ = = = 1110987628.)Ifm 6 7 , m 7 2 5,andm 11 6 +35,then=___.x xxx = = + = 29.)Ifm 8 7 2, m 7 4 7,andm 9 10 +3,then=___.x xxx = = =For#3031,a,b,c, and daredistinctcoplanarlines.Howareaandd related?30.) , ,a b b c c d P P 31.) , ,a b b c c d PFor#3233,findthemeasureofaninteriorangleandanexteriorangleofeachregularpolygon.32.) anoctagon 33.)apentagonCompletethetableforregularpolygons34.) (a)(b)(c)Work: (a) (b) (c)NumberofSides 6SumofexterioranglesMeasureofeachexteriorangle 20Measureofeachinteriorangle 162Sumofinteriorangles29 GraphingLinearEquations:35.) Grapheachlineusingtheslopeandyintercept:a)y=32x+1b)2x+y=4c)3x 2y=810987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y36.) Graph thelinesusingthexandyintercepts:a)2x+3y=6b)3x 5y=15c)2x 3y=1010 987654321 1 2 3 4 5 6 7 8 910x1098765432112345678910y37. Findthexandyinterceptofeachline:a)x+2y=6b)3x 4y=8c)y= 12 x+338. Findtheslopeandyinterceptofeachline:a)y=3x 5b)y=3c)3x 2y=439. Findtheintersectionofthetwolinesusingthesubstitutionoreliminationmethod.x+2y=8and2x+3y=1040. Explainwhythesetwolineswillnotintersecty=2x 1and8x 4y=16WritingLinearEquations: Writeanequationofthelinewith:41. yintercept2andslope4instandardform 42. xintercept4andyintercept2inslopeinterceptform43. through(1, 2)withslope3inslopeinterceptform44. through(6,2)andparalleltox 2y=5instandardform30 45. through(2, 1)andperpendiculartox+3y=7instandardform47. through(3, 2)and(7, 2)inslopeinterceptform49. xintercept3andyintercept5instandardform46. through(3,2)and(4,7)inslopeinterceptform48. through(4, 3)andwithxintercept2instandardform50. through(3, 3)andperpendicularto2x y=1inslopeinterceptformFor#5153,arethegivenlinesparallel,perpendicular,orneither?51.)1 232 6 10y xx y = + =52.)1 232 6 10y xx y = + + =53.)1 236 2 10y xx y = + =

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