Animate[{Plot[{Sin[x],m x},{x,-.2,.2}, PlotRange->{-.2,.2}, PlotStyle->{RGBColor[0,0,0],RGBColor[1,0,0]}],m},{m,-2,2}]

m=1.05
Plot[{Sin[x],m x},{x,-.01,.01},PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0]}]

Plot[Sin[x]/x,{x,-Pi,Pi},PlotRange->{-.2,1.2},PlotStyle->RGBColor[1,0,0]]