slope picture

The curve shows :

  • x goes 1 to right
  • y goes up by 3

the SLOPE is defined as the ratio of rise to the step

SLOPE = rise/step = 3/1 = 3

Now that :

  • Horizontal line has SLOPE of 0.
  • Vertical line has SLOPE of undefined.

It makes sense for me to imagine horizontal line has SLOPE of 0 since there is no rise at all. But why the vertical has SLOPE of undefined.?


1 Answer 1


Because $dx$ (step) for a vertical line is 0 and the expression for slope $$m=\frac{dy}{dx}$$ results in the bogeyman of mathematics, division by zero. That's why.

However, in some cases we define the slope of a vertical line as $\infty$. This implies $\frac 1{\infty}=0$ and vice versa, and is useful in projective geometry among other areas of mathematics.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .