How to find the slope of a vertical line?
Understand the Problem
The question is asking about the mathematical concept of slope, specifically how to determine the slope of a vertical line. It addresses the unique property of vertical lines in a Cartesian plane.
Answer
The slope of a vertical line is undefined.
Answer for screen readers
The slope of a vertical line is undefined.
Steps to Solve
- Define the Slope Formula
The slope of a line is generally calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ where $m$ is the slope, and $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
- Identify Points on a Vertical Line
For a vertical line, both points have the same $x$-coordinate. For example, if we consider points $(x_1, y_1)$ and $(x_1, y_2)$, the $x$-coordinates are the same.
- Insert Points into Slope Formula
Substituting these points into the slope formula: $$ m = \frac{y_2 - y_1}{x_1 - x_1} $$ The denominator becomes $0$, which leads to division by zero.
- Conclusion about the Slope of a Vertical Line
Since division by zero is undefined in mathematics, we conclude that the slope of a vertical line is undefined.
The slope of a vertical line is undefined.
More Information
Vertical lines do not have a defined slope because they do not run horizontally, meaning that there is no change in the $x$-coordinate even though the $y$-coordinate can change freely. This characteristic sets vertical lines apart from other types of lines in the Cartesian plane.
Tips
- Confusing the slope of vertical lines with horizontal lines. Remember, horizontal lines have a slope of $0$, while vertical lines have an undefined slope.
- Misapplying the slope formula by not recognizing that vertical lines involve division by zero.
