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 does a zero slope mean?
The line is perfectly horizontal — y never changes. Its equation is y = b, where b is a constant.
What is an undefined slope?
A vertical line has an undefined slope because the run is zero and you cannot divide by zero. Its equation is x = a constant.
Is a steeper line a bigger slope?
Yes. The greater the absolute value of the slope, the steeper the line. A slope of 5 is steeper than a slope of 1, and −5 is just as steep as 5 but falling.
Types of Slopes: Positive, Negative, Zero and Undefined
Every straight line has one of four kinds of slope. Knowing them lets you read a graph at a glance and predict how a line behaves.
| Type | What it looks like | Slope value | Example |
|---|---|---|---|
| Positive | Rises from left to right | m > 0 | A hill going up |
| Negative | Falls from left to right | m < 0 | A slide going down |
| Zero | Perfectly horizontal | m = 0 | A flat, level road |
| Undefined | Perfectly vertical | division by zero | A vertical cliff |
Positive slope
A positive slope means y increases as x increases — the line climbs as you read it left to right. The larger the number, the steeper the climb. A slope of 5 is much steeper than a slope of 1.
Negative slope
A negative slope means y decreases as x increases — the line falls left to right. A slope of −3 drops 3 units for every 1 unit you move right.
Zero slope
A horizontal line has a slope of exactly 0: there is no rise at all, so rise ÷ run = 0 ÷ run = 0. Its equation is y = b, a constant.
Undefined slope
A vertical line has an undefined slope. The run (x₂ − x₁) is zero, and dividing by zero is impossible. Its equation is x = a constant.
How to tell them apart quickly
- Going up to the right → positive.
- Going down to the right → negative.
- Flat → zero.
- Straight up and down → undefined.
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