Undefined Slope – Definition With Examples
Updated on November 27, 2025
In geometry and math classes, you’ll interact with graphs, coordinate planes, and slopes. There is much to learn about these geometric elements, and here at Brighterly, we do our best to help you master them!
In this exact article, we will discuss the undefined slope. An undefined slope is the slope of a vertical line. You might be wondering how this is undefined, if we know it is a vertical line, but we will enlighten you!
Here, we will cover the undefined slope meaning, its properties, and the difference between defined and undefined slopes. We are also going to share practice math problems with you so you can put this new information you have gained to the test.
What is undefined slope?
An undefined slope is the slope of a vertical line on a coordinate plane. The vertical line is considered an undefined slope because it doesn’t follow the general rules of slopes.
If you’re wondering, “What does an undefined slope look like?”, it’s a vertical line that runs up and down only.
Properties of slope
Slopes measure how steep or flat straight lines are in math and geometry. Here are their key properties:
- Slopes are defined by how much a line rises (i.e., goes up and down) and how much it runs (i.e., goes side to side)
- They can be positive, which means they run in an upward trajectory, or negative, which means they run in a downward trajectory
- A zero slope is a slope that runs from left to right with no rise
- An undefined slope runs from top to bottom, with no side movement
Properties of undefined slope
Undefined slopes have their own unique properties that set them apart from other types of slopes. They are:
- Undefined slopes are always straight, vertical lines that do not shift left or right, meaning they run parallel to the y-axis
- A vertical line crosses the x-axis at exactly one point, which is the constant x-coordinate.
- Slopes that are undefined can be expressed with the equation x = k, where k is the constant of the x-coordinate
Difference between defined and undefined slope
The difference between defined and undefined slopes is that the former have a numerical slope value and include any line that slants or runs horizontally across the graph. In contrast, the latter type belongs to a vertical line, which has no horizontal movement. Vertical lines run parallel to the y-axis and cannot be given a numerical slope because their “run” is zero.
Undefined slope examples
As an undefined slope is a vertical line, there are many examples of them in the world around us:
- The side of a building
- A street lamp
- A window frame
- A flagpole
- The legs of a table
When you’re working with slopes that are undefined in math class, the vertical lines on your coordinate plane are also a great example of undefined slope!
Undefined slope equation
The undefined slope equation is x = k, where k is the constant of the x-coordinate. This means that every point on your undefined slope has the same coordinates on the x-axis. It runs through every point on the y-axis, so no matter how much this changes, your undefined slope will remain the same. This equation is very easy to remember and use! It is a great foundational equation to learn before you move on to more complex slope equations in graphing and geometry.
Practice problems on undefined slope
Now is the time for you to try some practice problems on the concept. Simply grab a pen and some graphing paper, and work out the answers to our questions below. Putting yourself to the test once you have learnt this new information is a great way to see how well you have understood it and if you can apply it to real problems!
- Does the line x=5 have a defined or undefined slope line? Draw this slope on a coordinate plane or some graphing paper.
- Use the slopes of the lines y = 3 and x = 3 to compare and contrast the two lines.
- You have a line passing through the points (k,6) and (k,−4) with an undefined slope. Draw this line on your graphing paper.
Conclusion
Now you know all about the once-mysterious undefined slope graph, why it is considered undefined, and its unique properties. We have covered the definition of an undefined slope, provided you with an undefined slope example, and shared the associated equation with you. These slopes are just some small pieces of the geometry puzzle, and knowing this sets you up on a journey of success in your future learning.
Frequently asked questions on undefined slope
What is an undefined slope?
The undefined slope definition is a vertical line on a graph or coordinate plane. A vertical line passes through all points that share the same x-coordinate. This slope is undefined because there is no horizontal change, and it doesn’t follow the general rules of slope.
When is a slope undefined?
A slope is undefined when it is a vertical line. Vertical lines have no horizontal movement, so their slope cannot be calculated. Vertical lines do cross the y-axis (unless they are vertical lines outside the visible graph), but they never have a finite slope value.
How is the undefined slope different from a zero slope?
An undefined slope differs from a zero slope in orientation. An undefined slope is a vertical line, which has no horizontal change, so its slope cannot be calculated. A zero slope, on the other hand, is a horizontal line, which has no vertical change and a slope of 0.
Can a line with an undefined slope cross the y-axis?
Yes, a line with an undefined slope crosses the y-axis. This is because it covers every point on the y-axis as a never-ending vertical line. The key to remember with undefined slopes is that the slope cannot be calculated because the horizontal change (run) is 0.
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