A straight line is the locus of all those points which are collinear with two given points. Since, we know that one and only one line can be drawn from any two given points. Let and be two such given fixed points. Let be a point such that the points A, B and P always lie in the same straight line, then the locus of all such points will be the straight line through AB.
The position of a given straight line on a plane may be fixed in various ways and according to each way of fixing the position of a line we will get a definite form of the equation of the line.
a) We can have infinitely many lines through a given point.
b) To a given fixed direction, infinite many lines can be inclined each one of them passing through different points and also parallel to each other.
c) We can have one and only one line through a fixed point in a given direction.
d) One and only one line can be drawn through two given points.
General Equation of a Straight Line
Let be any two fixed points and be any general point on it such that the points A, B and P are always collinear, then according to condition of collinearity of three points.
which is the general equation of any straight line of one degree in two variables.