Equation of a line passing through the points A(x_{1} , y_{1}) and B(x_{2} , y_{2}) is (x  x_{1}) (y_{2}  y_{1}) = (y  y_{1}) (x_{2}  x_{1}).
Example:
Find the equation of line passing through (3,4) and (5,6).
Solution:
Formula for finding the equation of line when two points are given is
(x  x_{1}) (y_{2}  y_{1}) = (y  y_{1}) (x_{2}  x_{1}).
Given that,
(x_{1} , y_{1}) = (3,4)
(x_{2} , y_{2}) = (5,6)
Substituting these values in the formula, we get
(x  3) (6  4) = (y  4) (5  3)
(x  3) 2 = (y  4) 2
2x  6 = 2y  8
2x  2y + 2 = 0
Therefore, the 2x  2y + 2 = 0 is the required line.
Directions: Find the equation of the line, given two points. Also write at least 10 examples of your own.
