Algebraic equation of the form A

*x*+ B*y*+ C = 0, where A, B and C are real numbers and where A and B are not both zero.In the general form of the equation of the line A

*x*+ B*y*+ C = 0, the parameters A, B and C are usually non-zero real numbers, since:- if A = 0, then the line is horizontal (parallel to the x-axis);
- if B = 0, then the line is vertical (parallel to the y-axis);
- if C = 0, then the line passes through the origin (0, 0).

### Example

The equation 4*x* − 2*y* + 1 = 0 is the equation of a line whose slope is *m* = 2 and whose y-intercept is \(\frac{1}{2}\).

The equation of this line may be written in the functional form : *y* = 2*x* + \(\frac{1}{2}\).