terms:
:(exchanging the two points changes the sign of the left-hand side of the equation).

Determinant form

The two-point form of the equation of a line can be expressed simply in terms of a determinant. There are two common ways for that.

The equation is the result of expanding the determinant in the equation
:

The equation can be obtained by expanding with respect to its first row the determinant in the equation
:

Besides being very simple and mnemonic,