What Does Undefined Slope Mean

Undefined slope

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

Basically, a slope that is undefined looks like the lines on the coordinate system you encounter below:

When a gradient is undefined all you do is moving straight upwardly or direct downwards just. Y'all are non moving horizontally at all. In other words, the run is zilch. The slope is therefore at its steepest.

A adept real life example of undefined slope is an elevator since an elevator tin can only motility directly upwards or straight down.

It got its name "undefined" from the fact that it is incommunicable to carve up by zero.

Examples of undefined slope

Recall that 6/2 equal iii because 3 × 2 = half dozen

However, it is incommunicable to do 5/0 because there exist no number you lot can multiply 0 by to get 5. We say that this partition is undefined.

Now, let u.s.a. endeavour to go the slope for a couple of the lines above, say the line in the middle and the other line on the left.

For the line in the middle, the points are (one, iii) and (1, 9)

Let 10₁ = 1 , y_one = ix and 10₂ = 1 and y_ii = 3

chiliad = (y_i − y₂)/((x₁ − x_two)

m = (nine − 3)/(1 − ane)

m = 6/0

Since at that place exist no number you can multiply 0 by to get six, nosotros say that the slope is undefined.

For the line on the left, the points are (-3, iv) and (-3, ane)

Let x₁ = -3 , y₁ = four and x_ii = -3 and y_two = one

1000 = (y₁ − y_ii)/((ten₁ − 10₂)

m = (4 − ane)/(-3 − -3)

m = iii/0

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

Notice that for the line in the middle, the x-values are the aforementioned for both points (x_i = x_two = 1) . This is likewise the example for all the lines above.

In general, when the x-values or 10-coordinates are the same for both points, the slope is undefined. If you can brand this observation, there is no need to compute the slope.

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