hyplist={x≥0,y≥0,4x+y≤10,18x+15y≤66}
Manipulate[GraphicsGrid[{{Show[{Plot[0,{x,-5,10},PlotRange->{-5,10},Frame->True,AspectRatio->1],If[h1,{Graphics[{Blue, Thick,Line[{{0,-5},{0,10}}]},PlotRange->{{-5,10},{-5,10}}],Graphics[{Blue,Opacity[0.3],Rectangle[{0,-5},{10,10}]},PlotRange->{{-5,10},{-5,10}}]},{}],If[h2,Plot[0,{x,-5,10},PlotRange->{-5,10},PlotStyle->{Thick,Red},Filling->Top,FillingStyle->Directive[Opacity[0.3],Red]],{}],If[h3,Plot[10-4x,{x,-5,10},PlotRange->{-5,10},PlotStyle->{Thick,Green},Filling->Bottom,FillingStyle->Directive[Opacity[0.3],Green]],{}],If[h4,Plot[(66-18x)/15,{x,-5,10},PlotRange->{-5,10},PlotStyle->{Thick,Purple},Filling->Bottom,FillingStyle->Directive[Opacity[0.3],Purple]],{}]}],RegionPlot[Apply[And,Part[hyplist,Flatten[{If[h1,1,{}],If[h2,2,{}],If[h3,3,{}],If[h4,4,{}]}]]],{x,-5,10},{y,-5,10},Axes->True,PlotPoints->10,BoundaryStyle->Thick]}},ImageSize->600],{{h3,False,Style[hyplist[[3]],Large]},{True,False}},{{h4,False,Style[hyplist[[4]],Large]},{True,False}},{{h1,True,Style[hyplist[[1]],Large]},{True,False}},{{h2,True,Style[hyplist[[2]],Large]},{True,False}}]

Manipulate[Show[{Plot[0,{x,-1,5},PlotRange->{-1,5},Frame->True,AspectRatio->1],If[plot,Plot[(c-a x)/b,{x,-1,5},PlotRange->{-1,5},PlotStyle->{Red,Thick}],{}],Graphics[{Black,Disk[{0,66/15},.1],Style[Text["(0,66/15)",{0+.4,66/15+.3}],"Large"],Disk[{0,0},.1],Style[Text["(0,0)",{0-.4,0-.4}],"Large"],Disk[{2.5,0},.1],Style[Text["(2.5,0)",{2.5+.4,0-.4}],"Large"],Disk[{2,2},.1],Style[Text["(2,2)",{2+.4,2+.4}],"Large"]}],Graphics[{Blue,EdgeForm[Directive[Thick,Blue]],Opacity[0.3],Polygon[{{0,0},{2.5,0},{2,2},{0,66/15}}]},PlotRange->{{-5,10},{-5,10}}]},ImageSize->400],{{plot,True,Style["Show Line ax+by=k",Large]},{True,False}},{{a,1000,Style["Value of a",Large]},Range[-1000,1000,100]},{{b,500,Style["Value of b",Large]},Drop[Range[-1000,1000,100],{11}]},{{c,2000,Style["Slider for k",Large]},Range[-5000,5000,100],ControlType->Slider},{{c,2000,Style["Value of k",Large]},ControlType->InputField}]

(400,100), (-500,500)