You could find the rise, or height, that you would ascend. 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 X coordinate, being the denominator, will yield an undefined answer despite the value of the numerator. A zero slope is just the slope of a horizontal line! Another way to think of it is to examine the lines y = x, y = 2x, y=3x, y=4x, etc. An undefined slope (or an infinitely large slope) is the slope of a vertical line! is consistent with the usage in some books. is consistent with the usage in some books. Would you like to get a custom essay? So, undefined slope simply means the slope is enormous. So, there's your 1/0 again, which your algebra book called undefined, but your geometry calls it a line with infinite slope rather than undefined slope. What if you put something in the denominator that was incredibly small, so small that it was almost 0 but not quite? 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. 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. Vertical Lines. The slope is therefore at its steepest. Let’s say this cliff is only almost vertical. Notice that as the slope increases, the line gets closer and closer to being vertical, but never reaches it. Every point on the line has the same x value. What is Expanded Form in Math? Recall that 6/2 equal 3 because 3 × 2 = 6 The x-coordinate never changes no matter what the y-coordinate is! In this tutorial, learn about the meaning of undefined slope. Two examples are shown below. However, for a verticle line, the value of x is the same for every point on the line, so that x1 - x2 in the denominator is zero. In this situation, the difference between the two X points equals to zero. 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. Summary. It got its name "undefined" from the fact that it is impossible to divide by zero. The slope of a line is undefined if the line is vertical. You actually move forward one foot as you climb to the top. This cliff is pretty much vertical. Undefined Slope or Infinite Slope. Putting these numbers into the ‘rise over run’ slope formula, you get: That looks just fine. Two examples are shown below. We Will Write a Custom Essay SpecificallyFor You For Only $13.90/page! A vertical line has undefined, or infinite, slope. How about receiving a customized one? In this lesson, you will learn why the slope of a vertical line is called undefined or infinite. Unfortunately, this means "That vertical line has infinite slope. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. 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? Consider the line x = 2. Since division by 0 is undefined, the slope of the line is undefined. Imagine you are climbing a steep cliff. If the cliff has some incline to it, then you will travel forward while you climb. Monkey Face is about 400 feet high. I believe that "infinite slope" is a set phrase sometimes used to refer to vertical lines. – 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. When a line with undefined slope is graphed, it will look vertical, just like a steep cliff. In this tutorial, learn about the meaning of zero slope. In this situation, the difference between the two “X” points equals to zero. $\begingroup$ We would describe it as undefined, because a slope of $-\infty$ would also be vertical. I used the slope formula and found that the slope is undefined." The x-coordinate never changes no matter what the y-coordinate is! $\endgroup$ – Michael Burr Sep 16 '17 at 20:27 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. If you think of slope, or steepness, as rise over run, then the slope of her path is: Suppose now that you are very advanced in your rock climbing skills and you want to climb Monkey Face in Oregon. The slope of any line is (y1 - y2)/(x1 - x2). Okay, now let’s suppose that it wasn’t really a whole foot; it was only a tenth of a foot. The picture shows three vertical lines, all with undefined (infinite) slope. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! Vertical lines that go straight up and down have what is classed as undefined slope. Well, that slope would become enormous. The y-coordinate never changes no matter what the x-coordinate is! As the run, the denominator of the fraction, gets smaller and smaller, the slope gets bigger and bigger. You can probably see the pattern. 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. We have seen how the slope of a line may be undefined. An undefined slope is characterized by a straight, vertical line on the graph with the X coordinate points having no existing value of slope. 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. The closer the denominator gets to 0, the closer the whole fraction (the slope) gets to infinity. 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. Calculate the slope again: Again, that is huge, but imaginable. In this tutorial, learn about the meaning of undefined slope. It consists of an infinite set of points, all of which have 2 as the first value in the ordered pair. But we still wouldn't usually say "the slope is infinity". An undefined slope (or an infinitely large slope) is the slope of a vertical line! An undefined slope or infinite slope, means the line is neither moving to the left nor to the right such as the case of a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. until you remember that your mathematics teacher told you never to divide by zero. Vertical lines that go straight up and down have what is classed as undefined slope. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis 0. The equation of a line with undefined slope will look like x = ‘something.’, Copyright 2018 - Book Store WordPress Theme. There is no run! I used the slope formula and found that the slope is undefined." 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. The slope of a line is the steepness of the line. . In this tutorial, learn about the meaning of undefined slope. Since this is a vertical line, it has no slope. It is a rule that anything decided by zero is an undefined value since nothing can be divided by zero. So, undefined slope simply means the slope is enormous. Also, at a FS = 1.0, the maximum slope angle will be … In fact, many times it is called infinite slope. I believe that "infinite slope" is a set phrase sometimes used to refer to vertical lines. The slope of a vertical line is either + \,\infty or - \,\infty . In this situation, Mr. Piggy will experience the endless “fall” of his lifetime! If you attempt to find the slope using rise over run or any other slope formula, you will get a 0 in the denominator. Then, you get this: That’s a big slope, but it is something defined and real. A good real life example of undefined slope is an elevator since an elevator can only move straight up or straight down. You can't learn about linear equations without learning about slope. So, your rise is 400 feet. 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. However the way this is achieved is not very practical for a compiler writer as the syntactical requirement of an infinite loop is hard to maintain on the IR.

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