Statement 1: Two rays originating from two different points will trace a line if they head towards each other.
Statement 2: Two rays originating from a single point will trace a line if they travel in opposite directions.
Lets take two points A and B and rays moving towards each other as shown. Clearly, the path traced extends in both the directions, so it is a line.
Secondly, if two rays originate from the same point say 'O' and travel in opposite directions then they too trace a path extending to infinity in both directions, hence they trace a line as shown.