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:
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)
= 1 , y1
= 9 and x2
= 1 and y2
m = (y1
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
= 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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