What is the difference between a parametric equation and a general equation?

A parametric equation is defined by a variable t such as y = 4t +1 and x = 2t, while general equation is defined sorely by y and x (in 2 dimensional space). As t is the free variable you can simply replace t by x and build a general equation. In this case, y = 2x +1 since t = 1/2x.