Scratch

Graphics[{BSplineCurve[pts],Green,Line[pts],Red,Point[pts]}]

Show[Graphics[{BSplineCurve[pts],Green,Line[pts],Red,Point[pts]}],Axes->True]

Graphics[{Table[Line[{{i,-2},{i,6}}],{i,-2,8}],Table[Line[{{-2,i},{8,i}}],{i,-2,6}],Thickness[.015],Line[{{-2,0},{8,0}}],Line[{{0,-2},{0,6}}]}]
Export["Dropbox/Courses/201/201sp14/figures/ParametricAxes.png",
%,ImageResolution->100]

Graphics[{{Dashed,Table[Line[{{i,-2},{i,2}}],{i,-1,1}],Table[Line[{{-2,i},{2,i}}],{i,-1,1}]},{Table[Line[{{i,-2},{i,2}}],{i,-2,2,2}],Table[Line[{{-2,i},{2,i}}],{i,-2,2,2}]},Thickness[.015],Line[{{-2,0},{2,0}}],Line[{{0,-2},{0,2}}]}]
Export["Dropbox/Courses/201/201sp14/figures/ParametricAxes2.png",
%,ImageResolution->100]

Slides Graphics

pts={{-6,-3},{-6,0},{5,0},{5,3},{-3,3},{-2,6},{10,7},{13,9}};
Show[Graphics[{BSplineCurve[pts],Green,Line[pts],Red,Point[pts]}],Axes->True]
Show[Graphics[{Thickness[.01],Darker[Orange],BSplineCurve[pts]}],Axes->True,Ticks->None]
Export["Dropbox/Courses/201/201sp14/figures/Parametric.png",
%,ImageResolution->100]

pts={{-6,-3},{-6,0},{5,0},{5,3},{-3,3},{-2,6},{10,7},{13,9}};
Show[Graphics[{BSplineCurve[pts],Green,Line[pts],Red,Point[pts]}],Axes->True]
Show[Graphics[{Thickness[.01],Darker[Orange],BSplineCurve[pts],Text[Style["(x,y)=(f(t),g(t))",Large,Italic,FontFamily->"CMUSerif-Roman"],{8,5}],EdgeForm[{Black,Thick}],Disk[{7,6.9},.35]}],Axes->True,Ticks->None]
Export["Dropbox/Courses/201/201sp14/figures/Parametric2.png",
%,ImageResolution->100]

Components

x[t_]:=BSplineFunction[pts][t][[1]];
y[t_]:=BSplineFunction[pts][t][[2]];

Plot[x[t],{t,0,1}]

Plot[y[t],{t,0,1}]

Grid[{{ParametricPlot[{x[t],y[t]},{t,0,1}],Plot[x[t],{t,0,1}],Plot[y[t],{t,0,1}]}}]

Manipulate

Manipulate[
Show[{Graphics[{Line[{{x[0]-.5,y[0]-.5},{x[1]+.5,y[0]-.5},{x[1]+.5,y[1]+.5},{x[0]-.5,y[1]+.5},{x[0]-.5,y[0]-.5}}],Thickness[.01],Darker[Orange],BSplineCurve[pts],EdgeForm[{Black,Thick}],Disk[{x[t],y[t]},.35]},Axes->True,Ticks->None]
}],{t,0,1}]

Manipulate[
Grid[{{Rotate[Show[{Plot[x[t],{t,0,1},Axes->True,Ticks->None,Epilog->{PointSize[0.04],Point[{t,x[t]}]}]
},ImageSize->{300}],3Pi/2],},{Show[{Graphics[{Line[{{x[0]-.5,y[0]-.5},{x[1]+.5,y[0]-.5},{x[1]+.5,y[1]+.5},{x[0]-.5,y[1]+.5},{x[0]-.5,y[0]-.5}}],Thickness[.01],Darker[Orange],BSplineCurve[pts],EdgeForm[{Black,Thick}],Disk[{x[t],y[t]},.35]},Axes->True,Ticks->None]
},ImageSize->200],
Show[{Plot[y[t],{t,0,1},Axes->True,Ticks->None,Epilog->{PointSize[0.05],Point[{t,y[t]}]}]
},ImageSize->200]
}}],{t,0,1}]