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Special case of linear equations: Vertical lines

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Vertical Lines

An equation of the form x = c, where c is a constant, graphs as a vertical line: every point on the line has the same x-coordinate regardless of y. Because its run is zero, a vertical line has undefined slope. See a worked example graphing x = 2.

The vertical line x = c

An equation of the form x = c, where c is a constant, graphs as a vertical line. Every point on the line shares the same x-value, no matter what y is.

The equation x = 2 means every point on the line has an x-coordinate of 2: (2, -3), (2, 0), (2, 5) are all on the line. Since x never changes as y changes, the line runs perfectly straight up and down.

The vertical line x = 2 The equation x = 2 graphs as a vertical line: every point on the line has an x-coordinate of 2, no matter what y is. A vertical line has no slope. x y x = 2
The graph of x = 2, a vertical line.

Slope is rise over run, and a vertical line has a run of 0 — dividing by 0 is undefined, so a vertical line has no slope (it is not simply "zero"). This is the opposite extreme from a horizontal line, which has a slope of exactly 0, and it matters when checking whether two lines are parallel or perpendicular, since both comparisons rely on slope.

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