How to find whether a point is in a line or not Suppose in a given plain there are  fixed number of lines. A point P lies on one of the line. How to find which line intersects the point P ? I am giving an example 

In the above graph point P is on the line CE. We can determine it visually.But my problem is how to make the computer understand it. Is there any algorithm available to make it so ?
Any finite line is described by two points. assuming we are talking 2D here, then your graph can be described as a set of points, having X and Y coordinations, and a set of edges $E$, which describe which pair of points are connected with a line. Elementary geometry tell us the function expressing the points on these lines is $Y=(X-X_0)\frac{Y_1-Y_0}{X_1-X_0}+Y_0$ ($(X_0,Y_0), (X_1,Y_1)$ denote the two point's coordinations)

To check whether a point belongs to this line, insert the point's coordinates to the equation and see if the equation holds. since the line is not infinite, we should also check if the point is between the two points defining the line. If the equation holds, it is sufficient to check if one of the point's coordinates (say $X$) is between the two point's defining the line ($X_0$ and $X_1$).

So, for any line in the graph, perform the check explained above, if the above criteria holds, the line contains P.

Checking if P is on a specific line takes constant amount of computational effort, so the running time of this procedure is $O(E)$.