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.