Types of Slopes: Positive, Negative, Zero and Undefined
The four types of slope — positive, negative, zero and undefined — explained with values, pictures in words and examples.
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Frequently asked questions
What are the four types of slope?
Positive (rising), negative (falling), zero (horizontal), and undefined (vertical).
What is a positive slope?
A line that rises from left to right — y increases as x increases.
What is a negative slope?
A line that falls from left to right — y decreases as x increases.
What is a zero slope?
A horizontal line. There is no vertical change, so rise ÷ run equals zero.
What is an undefined slope?
A vertical line. The run is zero, and dividing by zero is undefined, so it has no slope value.
How do I remember zero vs undefined?
Horizontal lines (level ground) have zero slope; vertical lines (a sheer cliff) have undefined slope.
The four types of slope
Every straight line falls into one of four slope categories: positive, negative, zero or undefined. Knowing which type a line has tells you at a glance how it behaves — whether it rises, falls, stays level or goes straight up.
Positive and negative
A positive slope rises from left to right: as x increases, y increases (think of climbing a hill). A negative slope falls from left to right: as x increases, y decreases (heading downhill). The steeper the line, the larger the slope’s magnitude.
Zero and undefined
A zero slope is a flat, horizontal line — y never changes no matter how x moves, so rise ÷ run = 0. An undefined slope is a vertical line: the run is zero, and since you cannot divide by zero, the slope has no numerical value.
A simple memory aid: horizontal lines have a slope of zero (the ground is level), while vertical lines are undefined (a cliff has no "run"). The sign and size of a slope together describe a line’s direction and steepness completely.
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