Vertical line (geometry)

A vertical line is a straight line perpendicular to horizontal lines in a chosen coordinate system or reference frame. In Cartesian coordinates, it has constant x-coordinate and is parallel to the y-axis.

Cartesian coordinate system: A system that locates points using signed distances along perpendicular coordinate axes. Its axes provide the reference that defines vertical and horizontal directions.
Linear equation: An equation whose graph is a straight line in a coordinate plane. A vertical line is represented by an equation fixing the x-coordinate.
Horizontal line: A straight line parallel to the horizontal direction of a chosen reference frame. It is perpendicular to a vertical line in the same coordinate frame.
Vertical line test: A graph test for whether a curve represents a function of x: no vertical line may cross it more than once. The test uses vertical lines to check whether each x-value has at most one output.
Coordinate axis: A reference line in a coordinate system along which one coordinate varies while the others are fixed. A vertical line is parallel to one coordinate axis in the usual Cartesian plane.
x-coordinate: The signed horizontal position of a point in a Cartesian coordinate system. Every point on a vertical line shares the same x-coordinate.
Oblique line: A line that is neither horizontal nor vertical in the chosen coordinate frame. Unlike a vertical line, it has both horizontal and vertical displacement.
Function graph: The set of coordinate points representing the input-output pairs of a function. A vertical line can expose multiple outputs for one input on a plotted relation.
Slope: A measure of a line's steepness, usually expressed as vertical change divided by horizontal change. Vertical lines have zero horizontal change, so their slope is undefined.
Undefined slope: A slope value that cannot be expressed as a finite ratio because the horizontal change is zero. This is the algebraic consequence of a vertical line's orientation.

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Y-interceptCompared with: A vertical line on the y-axis meets it at infinitely many points, not a single intercept.