Use the definition of the Standard Form for the equation of a line.
A*x + B*y = C, where A, B, C are Real numbers such that A and B are not both zero.
A = l
B = m
C = 1
If you don't like that definition, solve the equation for y, and use the definition for the Slope-Intercept form.
There are at least three other definitions for straight lines that we could use.