Let `L_1 = a_1 x + b_1 y + c_1 = 0` and `L_2 = a_2x + b_2y + c_2 = 0`

Then, the general equation of any straight line passing

through the point of intersection of lines `L_1` and `L_2` is

given by `L_1 + lamdaL_2 = 0,` where `lamda in R`

These lines form a family of straight line

Also this general equation satisfies point of intersection

of `L_1` and `L_2` for any value of `lamda.`

Conversely, if a variable line is expressed in the form of `L_1 + lamda L_2 = 0 (lamda in R)` then it always passes

through fixed point which is the point of intersection of `L_1 = 0` and `L_2 = 0.`