You are watching: How to graph an undefined slope

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There space two special instances when it comes to lines in the xy plane. There is no any added information, these examples can be pretty confusing. But with a small instruction, they end up being some of the easiest lines to graph!

Zero steep

This class is ~ above what the heck zero slope and also undefined slope really mean. They"re sort of weird state that obtain really confusing and easy to mix up. For this reason let"s begin with what we know.

Lines the go up from left come right have a positive slope.

We understand that lines the go increase from left come right have actually a optimistic slope and lines that go down have a negative slope. Therefore if I have a steeper heat that"s walk up much more than it"s walking over, this heat maybe has a steep of 2, since it has actually a climb over a operation of 2/1. Together it gets a tiny bit flatter, perhaps it"s only going increase 1 because that every 1 it"s walking over, so now it has actually a steep of 1/1. Climate it it s okay a small bit flatter, so that goes end 2 and also up 1, therefore it has actually a steep of 1/2.

As it flattens out, the slope could get under to 0.01. Climate it flattens out even much more and it"s 0.001.Then it gets even flatter and it looks choose it"s virtually perfectly flat, yet the slope is still 0.0001. As it gets flatter and also flatter and flatter, the number gets smaller and smaller and smaller, till the allude where it i do not care perfectly flat and my slope access time 0.

A zero steep just way that it"s a perfectly level line. It"s horizontal. That doesn"t go up or down. It"s perfect flat.

together the steep flattens out, the is equal to 0.0001.

This makes sense, right? If it were to go down at all, mine slope would end up being -0.00001. And also then if it was a little bit an ext down, mine slope would certainly be -0.01. Then a little more would it is in -0.1. Then -1, -2, -5 or -10, everything we want.

So the zero slope is best in in between the an adverse slope lines and also the positive slope lines. It"s perfectly flat.

Then the inquiry becomes: what"s the equation of this line? This is an additional thing that"s really basic to obtain mixed up. However it turns out that the equation - I have to say the equations - of lines that have actually zero steep are always y equates to something .

There space two methods of thinking around this. One means is that it has actually a zero slope, for this reason you might use the slope-intercept kind and speak it"s y = 0x + b. In this case my y-intercept is 3, so it"s 0x + 3. That just means that y = 3, because 0 * x = 0.

But that requires you to know slope-intercept form, and there are a lot of other things going on, and also I normally prefer an ext intuitive ways. The method I think about this is that everywhere on this line, no issue where ns pick, y = 3, but x can be anything us want. X could be 4 or -1 or -3 or 10 or -5000. X have the right to be noþeles that us want, yet y always has to it is in 3. Therefore, my equation is y = 3. X deserve to be any kind of number, however y must constantly equal three. undefined Slope We can use comparable logic to figure out what the slope of a perfectly vertical line is, a line that goes right up and down. Again, let"s begin with a line that is sort of normal. It goes end 1 and also up 1. It"s gained a steep of 1/1, which is 1. Yet then it it s okay a tiny bit steeper, so this time it"s only going end 1, however it"s going up 2; for this reason it"s slope is 2/1, or 2. Then maybe it goes over 1 and also up 4, so its steep is 4.

Then that gets even steeper and it"s obtained a steep of 10, then possibly 100, perhaps 1,000,000. It usually looks prefer it"s walk up and down however it"s going a tiny little over. It"s simply super steep. It"s nothing you"d ever want to rise up. Yet it"s not fairly vertical.

Then, at the allude it access time vertical, the goes native 1,000,000 to 10,000,000 to 99,000,000 come infinity. Us hit the suggest where that doesn"t even come to be a number, but much more of just an idea. Since of that, we usually speak to the steep of vertical lines undefined.

We don"t really have a number that explains it. It"s sort of infinity. I like to think of the personally as infinity, but it"s really simply undefined. It"s not really a number. So, an undefined slope is a line the goes straight up and also down. It"s vertical. An unknown slope is a line the goes directly up and down; it is vertical. So then the inquiry becomes: what space the equations of these lines? together it turns out, this equations, instead of being y =, room going to it is in x = lines. Again, there are really two means to think about this.

You can either think about it as these equations don"t have a slope, so the regular slope-intercept form, y = mx + b, won"t do. It doesn"t have actually a slope, for this reason slope-intercept form is no good, which method it"s not y =, it"s x =.

But again, that"s sort of confusing and also I don"t personally use that way. I"d rather just think of the as: what room the various points on my line? Well, in ~ this point, x = -4 and y = -2. And also at this point, x = -4 and also y = 4. In ~ this point, x = -4 and also y = -5. Increase here, x might be -4 and y could be 100.

On every single one of these points that we pick, x = -4. Y have the right to be anything we want, yet x is always -4. Therefore, the equation of the is x = -4.

Lesson review

To review, we"ve gained two types of kind of monster lines: ones the go right left and right, which are horizontal, and ones that go straight up and also down, which room vertical. The horizontal ones have a slope of zero, since they"re best in in between the positives and the negatives. Their equations space y =, because no matter what, y is constantly the exact same thing.

Vertical lines have a slope of infinity or, more commonly, an undefined slope.

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They have equations that space x =, since no matter what, any point on the line has actually x at the exact same value. Y can be anything we want, yet x is constantly the same.