hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line. Parallel lines are lines in the same plane that never cross. Intersecting lines share a single point in common. Coincidental lines coincide with each other—every point that is on either one of them is also on the other. Perpendicular lines are lines that intersect at right angles. In three-dimensional space, skew lines are lines that are not in the same plane and thus do not intersect each other. In axiomatic systems The concept of line is often considered in geometry as a primitive notion in axiomatic systems, meaning it is not being defined by other concepts. In those situations where a line is a defined concept, as in coordinate geometry, some other fundamental ideas are taken as primitives. When the line concept is a primitive, the behaviour and properties of lines are dictated by the axioms which they must satisfy. In a non-axiomatic or simplified axiomatic treatment of geometry, the concept of a primitive notion may be too abstract to be dealt with. In this circumstance, it is possible to provide a description or mental image of a primitive notion, to give a foundation to build the notion on which would formally be based on the (unstated) axioms. Descriptions of this type may be referred to, by some authors, as definitions in this informal style of presentation. These are not true definitions, and could not be used in formal proofs of statements. The "definition" of line in Euclid's Elements falls into this category. Even in the case where a specific geometry is being considered (for example, Euclidean geometry), there is no generally accepted agreement among authors as to what an informal description of a line should be when the subject is not being treated formally. Definition Linear equation Lines in a Cartesian plane or, more generally, in affine coordinates, are characterized by linear equations. More precisely, every line (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero. Using this form, vertical lines correspond to equations with b = 0. One can further suppose either or , by dividing everything by