General Form of Equation of a Line
The "General Form" of the equation of a straight line is:
Ax + By + C = 0
A or B can be zero, but not both at the same time.
The General Form is not always the most useful form, and you may prefer to use:
The SlopeIntercept Form of the equation of a straight line: y = mx + b 

or 

The PointSlope Form of the equation of a straight line: y  y_{1} = m(x  x_{1}) 
Example: Convert 4x  2y  5 = 0 to SlopeIntercept Form
We are heading for
y = mx + b
Start with  4x  2y  5 = 0  
Move all except y to the left:  2y = 4x + 5  
Divide all by (2):  y = 2x  5/2  
And we are done! (Note: m=2 and b=5/2)
Why Use It?
It has the advantage of working well with vertical lines, which the SlopeIntercept Form and PointSlope Form do not.