To answer this question simply, the subsets of a line are the segments, the rays, and the points. They are commonly used in Mathematics, particularly in geometry.

Points are subsets of a line that follow the points on a graph through which said line runs. For example, if you were to draw up a graph plotting varying outside temperatures across the course of the days of a week, the subsets of the resulting graph line would be the points of information of each day, through which the line of the graph would flow through.

Segments are most commonly used in geology, and a line segment contains every point on the line between the end points it is bounded by. Examples of line segments include the sides of a triangle or square.

A ray is part of a line which is finite in one direction, but infinite in the other. It is defined by two points, the initial point, A, and one other, B. All the points in the line segment between A and B together with all points, C, on the line through A and B such that the points appear on the line in the order A, B, C is the line.

Points are subsets of a line that follow the points on a graph through which said line runs. For example, if you were to draw up a graph plotting varying outside temperatures across the course of the days of a week, the subsets of the resulting graph line would be the points of information of each day, through which the line of the graph would flow through.

Segments are most commonly used in geology, and a line segment contains every point on the line between the end points it is bounded by. Examples of line segments include the sides of a triangle or square.

A ray is part of a line which is finite in one direction, but infinite in the other. It is defined by two points, the initial point, A, and one other, B. All the points in the line segment between A and B together with all points, C, on the line through A and B such that the points appear on the line in the order A, B, C is the line.