The reason I said "in this case" was because in relativity, mass (or maybe more properly, momentum) is not constant with an increase in velocity.
In special relativity, the relation between mass and velocity is M=\frac{m}{\sqrt{1-\frac{v^2}{c^2}}.
Where M is the relativistic mass, and m is the...
You said yourself that the mass is constant. This means that for any point P(a,m) where a is acceleration and m is mass, you have the same y value (m) for any x value (a).
This is why you got a horizontal line when you graphed mass vs. acceleration; mass doesn't actually depend on the...