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Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`a$$], 0, "m"}, -10, 10}, {{ Hold[$CellContext`b$$], 5, "b"}, -15, 15}, {{ Hold[$CellContext`n$$], 50, "spray"}, 50, 400}}, Typeset`size$$ = { 621., {285.5, 291.5}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`a$$$4774$$ = 0, $CellContext`b$$$4779$$ = 0, $CellContext`n$4780$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`a$$ = 0, $CellContext`b$$ = 5, $CellContext`n$$ = 50}, "ControllerVariables" :> { Hold[$CellContext`a$$, $CellContext`a$$$4774$$, 0], Hold[$CellContext`b$$, $CellContext`b$$$4779$$, 0], Hold[$CellContext`n$$, $CellContext`n$4780$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Column[$CellContext`pts$$ = ListPlot[$CellContext`points$$ = RandomPoint[ ImplicitRegion[ And[$CellContext`y$$ == $CellContext`a$$ $CellContext`x$$ + \ $CellContext`b$$, -20 < $CellContext`x$$ < 20, -20 < $CellContext`y$$ < 20], {$CellContext`x$$, $CellContext`y$$}], Ceiling[$CellContext`n$$]], AxesOrigin -> {0, 0}, Axes -> True, PlotStyle -> { ColorData["SouthwestColors"][1]}, PlotLegends -> { PointLegend[{ ColorData["SouthwestColors"][1], Green, Magenta}, { Row[{"y", "=", If[$CellContext`a$$ != 0, Row[{ $CellContext`myPARAN[ Labeled[ Framed[$CellContext`a$$], "m", Top]], "x", "+", $CellContext`myPARAN[ Labeled[ Framed[$CellContext`b$$], "b", Top]]}], $CellContext`b$$]}], Row[{"y-Intercept", "=", "y(0)=b=", $CellContext`b$$}], $CellContext`point$$ = RandomChoice[$CellContext`points$$]; Row[{ Style[ Part[$CellContext`point$$, 2], Background -> Yellow], "=", If[$CellContext`a$$ != 0, Row[{ $CellContext`myPARAN[ Labeled[ Framed[$CellContext`a$$], "m", Top]], "\[Cross]", $CellContext`myPARAN[ Labeled[ Framed[ Part[$CellContext`point$$, 1]], "x", Top]], "+", $CellContext`myPARAN[ Labeled[ Framed[$CellContext`b$$], "b", Top]]}], Row[{$CellContext`b$$, " , y-coordinate of ", "(", Part[$CellContext`point$$, 1], ",", Style[ Part[$CellContext`point$$, 2], Background -> Yellow], ")"}]]}]}]}]; $CellContext`g1$$ = Graphics[{Magenta, PointSize -> Large, Point[$CellContext`point$$]}]; $CellContext`pts2$$ = ListPlot[$CellContext`points2$$ = RandomPoint[ ImplicitRegion[ And[$CellContext`y$$ < $CellContext`a$$ $CellContext`x$$ + \ $CellContext`b$$, -20 < $CellContext`x$$ < 20, -20 < $CellContext`y$$ < 20], {$CellContext`x$$, $CellContext`y$$}], Ceiling[10 $CellContext`n$$]], AxesOrigin -> {0, 0}, PlotStyle -> { ColorData["SouthwestColors"][1]}, PlotLegends -> { PointLegend[{ ColorData["SouthwestColors"][1], Green, Magenta}, { Row[{"y", "<", If[$CellContext`a$$ != 0, Row[{ $CellContext`myPARAN[ Labeled[ Framed[$CellContext`a$$], "m", Top]], "x", "+", $CellContext`myPARAN[ Labeled[ Framed[$CellContext`b$$], "b", Top]]}], $CellContext`b$$]}], Row[{"y-Intercept", "=", "y(0)=b=", $CellContext`b$$}], $CellContext`point2$$ = RandomChoice[$CellContext`points2$$]; Row[{ Style[ Part[$CellContext`point2$$, 2], Background -> Yellow], "<", If[$CellContext`a$$ != 0, Row[{ $CellContext`myPARAN[ Labeled[ Framed[$CellContext`a$$], "m", Top]], "\[Cross]", $CellContext`myPARAN[ Labeled[ Framed[ Part[$CellContext`point2$$, 1]], "x", Top]], "+", $CellContext`myPARAN[ Labeled[ Framed[$CellContext`b$$], "b", Top]], "=", Style[$CellContext`a$$ Part[$CellContext`point2$$, 1] + $CellContext`b$$, Background -> Yellow]}], Row[{$CellContext`b$$, " , y-coordinate of ", "(", Part[$CellContext`point2$$, 1], ",", Style[ Part[$CellContext`point2$$, 2], Background -> Yellow], ")"}]]}]}]}]; $CellContext`g2$$ = Plot[$CellContext`a$$ $CellContext`x$$ + $CellContext`b$$, \ {$CellContext`x$$, -20, 20}, PlotStyle -> {Dashed, Red}]; $CellContext`g4$$ = Graphics[{Magenta, PointSize -> Large, Point[$CellContext`point2$$]}]; $CellContext`pts3$$ = ListPlot[$CellContext`points3$$ = RandomPoint[ ImplicitRegion[ And[$CellContext`y$$ > $CellContext`a$$ $CellContext`x$$ + \ $CellContext`b$$, -20 < $CellContext`x$$ < 20, -20 < $CellContext`y$$ < 20], {$CellContext`x$$, $CellContext`y$$}], Ceiling[10 $CellContext`n$$]], AxesOrigin -> {0, 0}, Axes -> True, PlotStyle -> { ColorData["SouthwestColors"][1]}, PlotLegends -> { PointLegend[{ ColorData["SouthwestColors"][1], Green, Magenta}, { Row[{"y", ">", If[$CellContext`a$$ != 0, Row[{ $CellContext`myPARAN[ Labeled[ Framed[$CellContext`a$$], "m", Top]], "x", "+", $CellContext`myPARAN[ Labeled[ Framed[$CellContext`b$$], "b", Top]]}], $CellContext`b$$]}], Row[{"y-Intercept", "=", "y(0)=b=", $CellContext`b$$}], $CellContext`point3$$ = RandomChoice[$CellContext`points3$$]; Row[{ Style[ Part[$CellContext`point3$$, 2], Background -> Yellow], ">", If[$CellContext`a$$ != 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{-20, 20}}, ImageSize -> 300], Show[$CellContext`pts3$$, $CellContext`g2$$, $CellContext`g3$$, \ $CellContext`g5$$, AxesOrigin -> {0, 0}, Axes -> True, PlotRange -> {{-20, 20}, {-20, 20}}, ImageSize -> 300]}, Frame -> All], "Specifications" :> {{{$CellContext`a$$, 0, "m"}, -10, 10}, {{$CellContext`b$$, 5, "b"}, -15, 15}, {{$CellContext`n$$, 50, "spray"}, 50, 400}}, "Options" :> { TrackedSymbols :> {$CellContext`a$$, $CellContext`b$$, \ $CellContext`n$$}}, "DefaultOptions" :> {}], ImageSizeCache->{666., {389., 395.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`myPARAN[ Pattern[$CellContext`c, Blank[]]] := Which[ And[NumberQ[$CellContext`c] == True, $CellContext`c < 0], Row[{"(", TraditionalForm[$CellContext`c], ")"}], And[NumberQ[$CellContext`c] == True, $CellContext`c >= 0], TraditionalForm[$CellContext`c], NumberQ[$CellContext`c] == False, $CellContext`c]}; (SetOptions[ EvaluationNotebook[], PrivateNotebookOptions -> 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