slope intercept is great if you need to graph it.
general form is better if you are using it in a system of equations.

Linear equations are generally written in the
standard form of the line Ax + By = C where A, B and C are real numbers
and both of A and B are not equal to 0.

To solve a set of linear equations it may be required to convert one
of the equations to a form x = (C - By)/A or y = (C - Ax)/B which is
then substituted for either x or y in the other equation.

Also, it is quite easy to convert one form of the line to another
with a minimal amount of calculation. A system of linear equations can
be solved irrespective of which form of the line the equations are
originally in.