Undefined slope is so often misunderstood and many students find it confusing that I thought it would be a good thing to dedicate a special lesson to explain it.

Basically, a slope that is undefined looks like the lines below:

The slope is therefore at its steepest. A good real life example of undefined slope is an elevator.

It got its name "undefined" from the fact that it is impossible to divide by zero

Recall that 6/2 equal 3 because 3 × 2 = 6

However, it is impossible to do 5/0 because there exist no number you can multiply 0 by to get 5

We say that this division is undefined

Now, let us try to get the slope for one of the lines above, say the one in the middle

The points are (1, 3) and (1, 9)

Let x

m = (y

m = (9 − 3)/(1 − 1)

m = 6/0

Since there exist no number you can multiply 0 by to get 6, we say that the slope is undefined

Notice that the x-values is the same for both points (x

If you can make the above observation, there is no need to compute the slope