Definition: A ray is a part of a line that starts at one endpoint and extends forever in one direction, named by its endpoint first and then another point on it.
How do you name a ray?
Write the endpoint first. Ray AB starts at A and passes through B. Ray BA starts at B and goes the other way, so they are different rays. A small arrow over the letters shows the direction, pointing right.
Where do rays appear?
Rays form the sides of an angle, which is two rays sharing a common endpoint called the vertex. If two rays from the same point point in opposite directions, together they form a line.
Example. Points P, Q, R lie on a number line at 2, 9, and 15. Ray PQ contains Q and R, since it extends from 2 through 9 onward. Ray RQ starts at 15 and goes through 9 toward negative numbers, so it contains Q and P. These two rays overlap on the segment from 9 to 15 and are not equal.
What mistakes are common?
Naming the endpoint second, thinking a ray has a length, and calling ray AB and ray BA the same. A ray has no length, because it never ends. Opposite rays, like ray QP and ray QR when Q is between P and R, share only their endpoint.