Graphing A Line Of Intersection Between Planes

Define Equations Of Planes

p1[x_,y_]:=2*x+2*y-1; 

p2[x_,y_]:=4-x+y;

Plot Both Planes Using Plot3D Command

PlanePlot1 = Plot3D[p1[x,y],{x,-5,5},{y,-5,5}, PlotStyle->Red, PlotStyle->Red];

PlanePlot2 = Plot3D[p2[x,y],{x,-5,5},{y,-5,5} ,PlotStyle->Blue];

Show[PlanePlot1,PlanePlot2,PlotLabel->"Two Intersecting Planes", AxesLabel->{"X","Y","Z"},BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->{1,1,1}]

Define Equation of Line of Intersection & Plot

r[t_]:={0,5,9}+{1,-3,-4}*t;

LinePlot=ParametricPlot3D[r[t],{t,-5,5},PlotStyle->{Yellow,Thick},AxesLabel->{"X","Y","Z"},BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->{1,1,1}]

Plot Line and Intersection Planes on Same Graph

Show[PlanePlot1,PlanePlot2,LinePlot,PlotLabel->"Line of Intersection Formed By Two Planes", BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->{1,1,1} ]