# Equation of a Line

## Equation of a Line

Algebraic equation of the form Ax + By + 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 Ax + By + 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 4x − 2y + 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 = 2x + $$\frac{1}{2}$$.