This is part of a collection of definitions relating to the concept of Slope. Each of these definitions is a downloadable image, which can be easily incorporated into a lesson plan.
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In terms of the coordinates, it is the ratio in the difference in the y coordinates over the difference in the x coordinates.
To find the slope of the line that crosses these two points, use the slope formula. For the purposes of the slope formula, let's call these coordinates x1 and y1, and let's call these coordinates x2 and y 2.
Take those coordinates and plug them into the slope formula. y2 goes here and y1 goes here. x2 goes here and x1 goes here.
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Simplify the numerator and denominator. Then simplify the expression. The slope of the line that crosses these two points has a slope of 1.
So, what we've seen is that if two points have the same x-coordinate, then the line connecting them has an undefined slope.
Since the equation for any line can be written in slope-intercept form, as shown below, what happens when the slope is undefined?
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Recall that a ratio can look like a fraction and can be thought of as one number divided by another. What two numbers make up this ratio? As you can see from the definition, it’s the ratio of the change in y-coordinates over the change in x-coordinates.
Where do these change in coordinates come from? Take a look at this example. There are two points, each with its own coordinates.
Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math definitions on this topic. To see the complete collection of definitions, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resources can also be used with a screen reader. Follow these steps.The undefined slope is the slope of a vertical line. The x-coordinates do not change, no matter what y coordinates are. The vertical lines rise straight up or fall straight down, whereas they don't run left or right. The slope is the ratio of the change in y coordinates to the change in x coordinates. Since there is no change in x coordinates, for a vertical line, the denominator is zero which makes the slope undefined, or the slope cannot exist.
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The slope of a straight line is the tangent of its inclination to the x-axis and is denoted by ‘m’ i.e. if the inclination of a line is θ, its slope m = tan θ. The straight line that is either parallel to the y-axis or that coincides with the y-axis is the vertical line. For vertical lines, the angle of inclination θ = 90°, then slope m = tan 90° = undefined.
Another way to determine is slope = rise/run. For vertical lines, there is no run at all, thus making the denominator zero. We get an undefined slope. In other words, slope = \\(\\dfrac\\) = Change in y coordinates/ change in x-coordinates. When the x values are the same for the vertical lines, there could be no change in the value of x.
The slope of the y-axis or the slope of any straight line that is parallel to the y-axis is undefined since tan 90° is undefined. The equation of a straight line with an undefined slope is given as x = a, where a is any real number and it is a constant. It denotes that every point on the line has the x coordinates as 'a' throughout, regardless of the points picked. In particular, 'a' denotes the x-intercept, i.e., where the line crosses the x-axis.
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A few real-life examples that could be cited having undefined slope are the elevators that move only up and down, a mountain cliff that is vertical up to a finite distance that a mountaineer finds difficulty in climbing at, the skyscrapers, the lamp posts, or the flag posts, the sides of the doors or windows, the legs of the chair, the rocket at the time of launch and so on wherever we get to see vertical lines possible.
Any vertical line is parallel to the y-axis. A line parallel to the y-axis does not intercept the y-axis and hence, we cannot get any y-intercept of such a line. Thus, any line parallel to the y-axis cannot be expressed in the intercept form. The following is the graphical representation of the undefined slope of the lines x = -5, x = 0 , x = 3 and x = 5.
We know that a vertical line is a perpendicular line to the x-axis that has an undefined slope. If we have a pair of coordinates, (x
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) through which a line passes, it is evident that the x-coordinates are the same. They are the points on the same vertical line. Thus the slope of such a line will be undefined.
The horizontal lines that are parallel to the x-axis have a Zero Slope, whereas the vertical lines that are parallel to the y-axis have an undefined slope. The graph of a line with zero slope is y = b, whereas that with an undefined slope is x = a, where 'b' and 'a' are y and x-intercepts respectively.
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The undefined slope is the slope of any vertical line that goes up or down. There is no horizontal movement and hence the denominator is zero while calculating the slope. Thus the slope of the line is undefined.
The slope of a straight line is the trigonometric tangent of the angle θ that the line makes with the positive direction of the x-axis. The lines that are parallel to the y-axis, are perpendicular to the x-axis. Thus the inclined angle is 90° and tan 90° = undefined. The equation of undefined slope is that of a vertical line that is x = a, where a is the x-intercept or any constant.
We calculate the rise over run and find that there is no run or no change in x coordinates. Thus we determine that the slope is undefined as the denominator becomes zero in the fraction.
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The Undefined slope graph is a line parallel to the y-axis or perpendicular to the x-axis. Thus there is no y-intercept and there is no change in the x-coordinates. The x values of the points on this line remain the same.
An example for an undefined slope could be a line passing through the points (4, -5) and (4, 8). The slope of a line passing through the points is given as \\(\\dfrac\\). Thus we have \\(\\dfrac\\)= 13/0 is undefined.
Yes, any line parallel to the y-axis has an undefined slope as the angle of inclination to the x-axis is 90°. Slope = tan 90° = undefined.
Undefined & Zero Slope Graph
No. A zero slope is that of a horizontal line. A slope is undefined for a vertical line. Any line parallel to the y-axis has an undefined slope.
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