chapter 3 – graphing linear equations - wordpress.com · 3.2 graphing linear equations ex: list...
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Chapter3–GraphingLinearEquationsRectangularCoordinateSystemCartesianCoordinateSystemOriginQuadrantsy-axisx-axisScaleCoordinates
Ex:Ploteachpoint:(0,0),(-1,3),(1,3),(1,-3),(-1,-3)
Ex:Givethecoordinatesofeachpoint:
Ex:(#22)Giventhefollowinggraphthatgivestheheartrateofawomanbefore,duringandafteranaerobicworkout.
a)Whatwasthewoman’sheartratehalfanhourafterbeginningtheworkout?b)Forhowlongdidthewomanworkoutathertrainingzone?
3.2GraphingLinearEquationsEx:Listpairsofnumbersthatsatisfytheequationy=x+1byconstructingatableofvalues:c)Does(4,4)satisfythatequation?Howabout(5,-5)?d)Plotthosepairsonarectangularcoordinatesystem.Doyouseeapattern?
Ex:Graph2x–y=-3bysolvingforyfirstandthensettingupatableofvalues.
3.3InterceptsEx:Graphtheliney=3x–6byfindingthex-andy-interceptsandusingonemorepointasacheck.
HorizontalandVerticalLinesEx:Graphy=3bysettingupatableofvalues.
Ex:Graphx=-3bysettingupatableofvalues.
Ex:(Ex8)Usinginformationabouta2010ToyotaPriusHybrid,wecansetuptheequation 12m+600g=7200wheremrepresentsthenumberofmilesdriven,andgrepresentsthenumberofgallonsofgasleftinthetank.Findtheinterceptsforthislineandexplainwhattheyrepresent.
3.4SlopeandRateofChangeEx:Pretendyouaregoingtogoskiingdownamountain.Drawexamplesofthefollowing:a)averysteepslopeb)aslightlysteepslopec)aflatslopeQuestion:Howcouldwedifferentiatebetweengoingupamountainandgoingdownamountain?Question:Howcouldwequantifyhowsteeptheslopesare?
Slope=!"#$!%&
= )*+&,$"&-)*+&,$"&.
Ex:Graphy=2x–1andthen,usingtriangles,calculatetheslopebetween:
a)x=0andx=2 b)x=2andx=6 c)x=-5andx=1Whatdoyounoticeaboutallthreeslopes?
UsingtheSlopeFormulaTheslopeofthelinepassingthrough(x1,y1)and(x2,y2)isgivenbytheformula:
slope=m=-/0-1./0.1
Ex:Usingtheslopeformula,findtheseslopes:1)Theslopeofthelinepassingthrough(-1,3)and(2,6)2)Theslopeoftheliney=33)Theslopeofthelinex=3
ParallelandPerpendicularLinesParallelLines:PerpendicularLines:Ex:Fillinthischart:
Slope ParallelSlope PerpendicularSlope
2
3
12
34
−56
-6
0
Ex:Determinewhetherthelinesthrougheachpairofpointsareparallel,perpendicular,orneither.1) (3,3)and(4,4) (3,3)and(2,4)2) (2,4)and(-1,-1) (8,0)and(11,5)
3.5Slope-InterceptFormIfyouhaveanequationofalineinthisform: 2x–y=5andyousolvefory:thenyouhaveSlope-InterceptForm,whereEx:Findtheslopeandthey-interceptofthelinewithequation 9x–3y=10Ex:Writeanequationofthelinewithslope=-2andy-intercept(0,5.4)
Ex:Useslope-interceptformtograph 2x+2y=-6
Ex:Determinewhetherthegraphsofy=4x+6andx+4y=-2areparallel,perpendicularorneither.
Ex:(#100)AnewPlaystation3costs$310.50andmembershipinanonlinevideogamemultiplayernetworkcosts$18.49permonth.a)Writealinearequationthatgivesthecostforsomeonetobuythemachineandbelongtotheonlinenetworkformmonths.b)Useyouranswerinpartatofindthecosttobuythemachineandbelongtothenetworkfor3years.
3.6Point-SlopeFormm=Point-SlopeForm:y–y1=m(x–x1)Ex:Findanequationofthelinethathasslope5andpassesthrough(-1,13).Writetheanswerinslope-interceptform.
Ex:Findanequationofthelinethathasslope0andpassesthrough(3,4).Ex:Findanequationofthelinethatpassesthrough(4,2)and(-1,12).Writetheanswerinslope-interceptform.
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