How can I tell if a point belongs to a certain line?

Question

How can I tell if a point belongs to a certain line?

Examples are appreciated, if possible.

Answer 1

In the simplest form, just plug the coordinates into the line equation and check for equality.

Given:

Point p (X=4, Y=5)
Line l (Slope=1, YIntersect=1)

Plug in X and Y:

   Y = Slope * X + YIntersect
=> 5 = 1 * 4 + 1
=> 5 = 5

So yes, the point is on the line.

If your lines are represented in (X1,Y1),(X2,Y2) form, then you can calculate slope with:

 Slope = (y1 - y2) / (x1-x2)

And then get the Y-Intersect with this:

 YIntersect = - Slope * X1 + Y1;

Edit: I fixed the Y-Intersect (which has been X1 / Y1 ...)

You'll have to check that x1 - x2 is not 0. If it is, then checking if the point is on the line is a simple matter of checking if the Y value in your point is equal to either x1 or x2. Also, check that the X of the point is not 'x1' or 'x2'.