intercepts=Range[-4,4,.1];Animate[Animate[Plot[j/(x+k),{x,-4,4},PlotRange->{-10,10},PlotLabel->"y = "<>ToString[j]<>"/(x + "<>ToString[k]<>")",PlotStyle->{Thickness[0.01],Hue[(Position[intercepts,k]//Flatten//First)/9]}],{j,intercepts}]
,{k,intercepts}]