Well, that slope would become enormous. Every point on the line has the same x value. What if you put something in the denominator that was incredibly small, so small that it was almost 0 but not quite? . In this situation, Mr. Piggy will experience the endless “fall” of his lifetime! The x-coordinate never changes no matter what the y-coordinate is! But then you measure even more carefully, and you find that the true distance you move forward as you climb Monkey Face is really 0.0001 feet. This cliff is pretty much vertical. The equation of a line with undefined slope will look like x = ‘something.’, Copyright 2018 - Book Store WordPress Theme. Let’s say this cliff is only almost vertical. Undefined Slope or Infinite Slope. Notice that as the slope increases, the line gets closer and closer to being vertical, but never reaches it. The slope of any line is (y1 - y2)/(x1 - x2). In fact, many times it is called infinite slope. – Definition & Examples, Writing Ionic Compound Formulas: Binary & Polyatomic Compounds, Graphing Undefined Slope, Zero Slope and More, Bacterial Transformation: Definition, Process and Genetic Engineering of E. coli, Rational Function: Definition, Equation & Examples, How to Estimate with Decimals to Solve Math Problems, Editing for Content: Definition & Concept, Allosteric Regulation of Enzymes: Definition & Significance. In this lesson, you will learn why the slope of a vertical line is called undefined or infinite. If you think of slope as rise over run, then the line rises an infinite amount, or goes straight up, but does not run at all. Unfortunately, this means "That vertical line has infinite slope. Occasionally, you might also hear the phrase ‘no slope,’ but that isn’t a good description because it can easily be confused with a flat or horizontal line, which has zero slope. The slope is therefore at its steepest. The closer the denominator gets to 0, the closer the whole fraction (the slope) gets to infinity. An undefined slope (or an infinitely large slope) is the slope of a vertical line! If we try to find the gradient/slope of a vertical line with the gradient formula, the result is an undefined answer, as 0 will be the denominator. You actually move forward one foot as you climb to the top. Vertical Lines. The line in the undefined slope doesnt move to the left or the right along the Y axis. But we still wouldn't usually say "the slope is infinity". Positive slope – the line rises from left to right. You may be able to guess that vertical lines are lines that go straight up and down, but did you know that all vertical lines have the same slope? The y-coordinate never changes no matter what the x-coordinate is! It consists of an infinite set of points, all of which have 2 as the first value in the ordered pair. An undefined slope is characterized by a straight, vertical line on the graph with the “X” coordinate points having no existing value of slope. The slope is said to have reached limit equilibrium when FS=1.0. Calculate the slope again: Again, that is huge, but imaginable. In this situation, the difference between the two X points equals to zero. In fact, many times it is called infinite slope. You will be climbing straight up with no forward movement at all. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. The x-coordinate never changes no matter what the y-coordinate is! is consistent with the usage in some books. Monkey Face is about 400 feet high. Also, at a FS = 1.0, the maximum slope angle will be … There is no run! Note that it is essential that n and i are unsigned as overflow on signed int gives undefined behavior and Putting these numbers into the ‘rise over run’ slope formula, you get: That looks just fine. Vertical Lines. One thing you may notice is that all the lines have equations that look like x = ‘something.’ Just like a vertical cliff face, a vertical line does not progress in the horizontal, or x, direction. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! Well, the more accurate thing to say about division by zero is that it is undefined, which sounds a lot like ‘we don’t know the answer.’ If you play with numbers a little, however, you can get an idea of what is happening. In this tutorial, learn about the meaning of zero slope. Unfortunately, this means "That vertical line has infinite slope. You were probably told it can’t be done, and that if you tried the universe would implode or you would never again find a date or something else horrifyingly catastrophic. You do not move forward at all as you climb. I used the slope formula and found that the slope is undefined." We have seen how the slope of a line may be undefined. This is "undefined", because you can't divide by zero. If you want to calculate the slope, or steepness, of this cliff, you would follow the same process as with the more gently sloping cliff. So, your rise is 400 feet. The slope of a line is undefined if the line is vertical. Another way to think of it is to examine the lines y = x, y = 2x, y=3x, y=4x, etc. I used the slope formula and found that the slope is undefined." I believe that "infinite slope" is a set phrase sometimes used to refer to vertical lines. You could find the rise, or height, that you would ascend. A good real life example of undefined slope is an elevator since an elevator can only move straight up or straight down. There is no run! $\endgroup$ – Chickenmancer Sep 16 '17 at 20:26 $\begingroup$ We might call it infinite if we treat $+\infty$ and $-\infty$ as the same (a projective space). Then, you get this: That’s a big slope, but it is something defined and real. But we still wouldn't usually say "the slope is infinity". Let’s review. Since division by 0 is undefined, the slope of the line is undefined. Therefore, the slope formula will always result in division by zero and therefore the slope will be undefined. If we try to find the gradient/slope of a vertical line with the gradient formula, the result is an undefined answer, as 0 will be the denominator. So, undefined slope simply means the slope is enormous. For an infinite slope analysis, the FS is independent of the slope depth, h, and depends only on the angle of internal friction, φ, and the angle of the slope, β. The slope of a line is the steepness of the line. Would you like to get a custom essay? In this picture, the climber ascends 8 meters while she travels forward 5 meters. You could also say that the line as "no slope" (not to be confused with a slope of 0, which I'll get to in a minute). In this situation, the difference between the two “X” points equals to zero. The X coordinate, being the denominator, will yield an undefined answer despite the value of the numerator. There are many ways to think about slope. Okay, now let’s suppose that it wasn’t really a whole foot; it was only a tenth of a foot. What is Expanded Form in Math? How about receiving a customized one?

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