From almost everywhere, a straight line is linear defined as $C(t)=P_0+tV_0$. And I am wonder what does a straight line but is not linear by the means of the parameter $t$. For example $C(t)=P_0+tV_0+t^2V_0+t^3V_0$.
So would it means a straight line is not really needed to be linear? Would that be the case that the definition for a straight line is: For any two points $p=C(a),q=C(b)$,