Undefined slope

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:

Examples of undefined slope
All you do is moving straight up or straight down only. You are not moving horizontally at all. In other words, the run is zero

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 x1 = 1 , y1 = 9 and x2 = 1 and y2 = 3

m = (y1 − y2)/((x1 − x2)

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 (x1 = x2 = 1) . This is also the case for all the lines above

In general, when the x-values or x-coordinates is the same for both points, the slope is undefined

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

Take the undefined slope quiz below to see if you really understood this lesson.

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