What is Undefined Slope?
Undefined slope refers to a situation in which the slope of a line or curve cannot be determined or expressed as a finite numerical value. Undefined Slope typically occurs when the change in the vertical direction becomes infinitely large compared to the horizontal direction. For example, if we have any vertical line, slope of this line is undefined as with no change in horizontal direction there is infinitely large change in vertical direction.
In mathematics, the slope of a line is typically calculated as the ratio of the change in the vertical direction (the “rise”) to the change in the horizontal direction (the “run”). If the run is zero, which is the case for a vertical line, you cannot calculate a finite slope because division by zero is undefined in mathematics.
Undefined Slope Definition
Slope of a line is defined as the ratio of the change in the vertical direction (y-coordinates) to the change in the horizontal direction (x-coordinates) between two points on the line.
When change is y-coordinate becomes infinitely large compare to change in x-coordinate, thus the slope is undefined for that curve or line.
How to Find Slope?
Slope is calculated by dividing the difference in vertical (y) values by the difference in horizontal (x) values i.e., Δy/Δx. When there’s no change in the horizontal values (x) along the line, the slope becomes undefined. Slope is determined by the difference in vertical (y) values divided by the difference in horizontal (x) values. It becomes undefined when there’s no change in the horizontal values (x) along the line.
Lets take an example of an undefined slope: A line that goes through the points (1, 0) and (1, 1). If we use these values in the slope formula: (1-0)/(1-1) = 1/0, here we get an undefined result.
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Undefined Slope
Undefined Slope as the name suggests is the slope of any curve or line where the change in vertical direction became exponentially too large compared to horizontal direction. Undefined Slope of any line or curve becomes increasingly steep, and its slope cannot be expressed as a finite numerical value.
In this article, we will discuss about undefined slope in detail along with the equation for undefined slope and how we can identify the undefined slope in graphs. We will also see some solved examples and practice problems on undefined slope equations.
Table of Content
- What is Undefined Slope?
- Undefined Slope Equation
- Undefined Slope Graph
- How To Find The Undefined Slope?
- Zero Slope vs Undefined Slope
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