Positive, Negative, Zero, or Undefined Slope

Identify the slope type

To classify a slope, look at how the line changes as you move from left to right.

1. Positive slope: the line rises from left to right.
2. Negative slope: the line falls from left to right.
3. Zero slope: the line is horizontal.
4. Undefined slope: the line is vertical.

How to decide

If you are given two points, compare the change in y and the change in x:

• If both changes have the same sign, the slope is usually positive.
• If the changes have opposite signs, the slope is negative.
• If the change in y is 0, the slope is zero.
• If the change in x is 0, the slope is undefined because division by zero is not allowed.

Quick check

You can check your answer by sketching the line or imagining the graph:

• rising = positive
• falling = negative
• flat = zero
• straight up and down = undefined

When the exercise asks for the final answer, give only the correct slope type and simplify any expression used to find it.