Standard-Form-of-Linear-Equation

STANDARDFORMOFALINEAREQUATIONTheequation23yxiswritten_______________form.Ifwemove“2xwehave_______________________.”totheothersideoftheequation,23yxslopeintercept2x23xy23xyIfwemove“2xwehave_______________________.”totheothersideoftheequation,23xyThisisstilla________equation,butitiswritteninadifferentform.linearAlinearequationintheform_______________isin______________,whereA,B,andCareintegers.AxByCstandardformAlinearequationintheform_______________isin______________,whereA,B,andCareintegers.AxByCstandardformRememberthesetofintegersis....4,3,2,1,0,1,2,3,4...NOFRACTIONS!!!NODECIMALS!!!Example1:A.Jackieisinchargeofsellingticketsfortheschooljazzconcertat$2.00forstudentsand$4.00foradults.Shehopesthatthetotalticketsaleswillbeabout$600inordertocoverexpensesandmakeamodestprofit.Writealinearequationinstandardformtomodelthissituation.Letxy#studenttickets#adulttickets$2.00$4.002.004.00600xy24600xyB.Adonationof$300wasmaketotheClassicalMusicClubforthepurposeofbuildingtheircollectionofCDs.Atthelocalmusicstore,someclassicalCDscost$10andothercost$15.Theclubwantstoknowhowmanyofeachtypecanbuywiththe$300.(Donotconsidersalestax.)Writeanequationinstandardformtomodelthissituation.Letxy#classicalCDs#otherCDs$10.00$15.0010.0015.00300xy1015300xy524yxx-term+y-term=constantNofractions,nodecimals!422xy587yx253xy735xy7.54.3xyABCDEFExample2:Tellwhethertheequationsbelowareinstandardform.NOYESNONOYESNOFRACTIONSDECIMALSIfanequationisnotwritteninstandardform,wecanrewritetheequationsothatitisinstandardform.Example3:Writeeachlinearequationinstandardform.A.5724yxB.387yx2y5742xy4257xy7777356yx3x3756xy3756xy4257xyC.5724yxD.53574053xy5742xy2y4257xy4257xy574053xy5.75.34xy101010575340xy40yWecanfindthe___&___interceptsandthe________whentheequationiswritteninstandardform.xyslopex-interceptisatyy-interceptisatx(2,0)0(0,3)0x-interceptisatyy-interceptisatx(2,0)0(0,3)0Weknowthaty=0atthe____intercept,sowecanplugin0for___tofindthe_____intercept.Weknowthatx=0atthe____intercept,sowecanplugin0for___tofindthe_____intercept.xyxyyxExample4:Findthex&yinterceptsofthefollowingequations.A.4212xyx-intercepty-interceptPlugin0foryPlugin0forx04212x412x443xintercept3,0x41022y212y226yintercept0,6yExample4:Findthex&yinterceptsofthefollowingequations.B.x-intercepty-interceptPlugin0foryPlugin0forx23180x218x229xintercept9,0x23108y318y336yintercept0,6y2318xyExample4:Findthex&yinterceptsofthefollowingequations.C.x-intercepty-interceptPlugin0foryPlugin0forx0AxBCAxCAACxAintercept,0CxA0AByCByCBBCyBintercept0,CyBAxByCx-intercepty-interceptCxAintercept,0CxACyBintercept0,CyBAxByCWriteinslope-interceptformtofindtheslope.AxByCAxByCAxByAxCBBBACyxBBx-intercepty-interceptCxAintercept,0CxACyBintercept0,CyBAxByCAmBx-intercept=y-intercept=Slope=AxCByBAx-intercept=y-intercept=Slope=CAAxCByTofindthex-intercept,crossoutthey-term…BAx-intercept=y-intercept=Slope=CAAxCByBATofindthey-intercept,crossoutthex-term…CB-3212xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.A.A=B=C=3212Slopex-intercepty-interceptAmB32m32mExample5:Findtheslopeandx&yinterceptsofthefollowingequations.A.-3212xyA=B=C=3212Slopex-intercepty-interceptAmB-intCxA32m32m3-int12x-int4xExample5:Findtheslopeandx&yinterceptsofthefollowingequations.A.-3212xyA=B=C=3212Slopex-intercepty-interceptAmB-intCxA-intCyB32m32m3-int12x-int4x-int122y-int6yExample5:Findtheslopeandx&yinterceptsofthefollowingequations.A.-3212xyA=B=C=3212Slopex-intercepty-interceptAmB-intCxA-intCyB32m32m3-int12x-int4x-int122y-int6yExample5:Findtheslopeandx&yinterceptsofthefollowingequations.B.A=B=C=5330Slopex-intercepty-interceptAmB53m53m5330xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.B.A=B=C=5330Slopex-intercepty-interceptAmB53m53m5330xy-intCxA-int305x-int6xExample5:Findtheslopeandx&yinterceptsofthefollowingequations.B.A=B=C=5330Slopex-intercepty-interceptAmB53m53m5330xy-intCxA-int305x-int6x-intCyB3-int30y-int10yExample5:Findtheslopeandx&yinterceptsofthefollowingequations.B.A=B=C=5330Slopex-intercepty-interceptAmB53m53m5330xy-intCxA-int305x-int6x-intCyB3-int30y-int10y4612xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.C.A=B=C=4612Slopex-intercepty-interceptAmB46m23m4612xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.C.A=B=C=4612Slopex-intercepty-interceptAmB46m23m-intCxA2-int14x-int3x4612xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.C.A=B=C=4612Slopex-intercepty-interceptAmB46m23m-intCxA2-int14x-int3x-intCyB2-int16y-int2y4612xyExample5:Findtheslopeandx&yinterceptsofthefollowingequations.C.A=B=C=4612Slopex-intercepty-interceptAmB46m23m-intCxA2-int14x-int3x-intC