Hold the expression using With and insert a value for a
With[{a = 1},
Plot[{a M1 + a M1^3.4}, {M1, 1, 100}, PlotRange -> Automatic]
]
Same thing can be done, instead of setting the value for Mc
With[{Mc = 54},
ee[M_] := If[M < Mc, M, M^3.4];(*ee is viscosity[\eta]*)
Plot[ee[M], {M, 1, 100}, Filling -> Axis]
]
Make the EE functions of two arguments, then supply the value of a using the manipulator
EE1[M1_, a_] := a M1;
EE2[M1_, a_] := a M1^3.4;
Manipulate[
Plot[EE1[M1, a] + EE2[M1, a], {M1, 1, 100}, PlotRange -> {0, 2*^7}],
{a, 1, 3}]
