Conic Sections - The Line

On an (x, y) graph a line can have the shape to the left.

If a plane intersects the cone when it is slanted the same as the side of the cone, (formally, when it is parallel to the slant height), and when it passes through the tip of the cone, (formally when it passes through the vertex), the conic section is a line. This is shown to the left.

This link will take you to an interactive 3D virtual reality world depicting a line as the intersection of a cone and a plane.

Here is a picture that shows how to form a line by intersecting a cone and a plane.