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Special case of linear equations: Horizontal lines

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Horizontal Lines

An equation of the form y = c, where c is a constant, graphs as a horizontal line: every point on the line has the same y-coordinate regardless of x. A horizontal line has a slope of 0. See a worked example graphing y = 3.

The horizontal line y = c

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

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

The horizontal line y = 3 The equation y = 3 graphs as a horizontal line: every point on the line has a y-coordinate of 3, no matter what x is. x y y = 3
The graph of y = 3, a horizontal line at height 3.

A horizontal line has a slope of 0, since y never rises or falls as x changes. This is the special case at one end of the slope spectrum; a vertical line is the special case at the other end, where slope is undefined. Slope also governs when two lines are perpendicular, and it is the same slope you compute from the slope formula.

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