If a line is vertical, its slope is?
Understand the Problem
The question is asking about the slope of a vertical line. It seeks to clarify the mathematical property of vertical lines in coordinate geometry.
Answer
The slope of a vertical line is undefined.
Answer for screen readers
The slope of a vertical line is undefined.
Steps to Solve
- Identifying a vertical line's properties
A vertical line has the same x-coordinate for all points on it and can be represented by the equation $x = a$, where $a$ is a constant.
- Understanding slope formula
The slope $m$ of a line is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
- Calculating slope for a vertical line
For a vertical line, let's take two points on it. For example, the points $(a, y_1)$ and $(a, y_2)$. Substituting these points into the slope formula gives:
$$ m = \frac{y_2 - y_1}{a - a} $$
Since the denominator $a - a$ equals $0$, the slope calculation results in division by zero.
- Conclusion about vertical line slope
A division by zero is undefined in mathematics, which means that the slope of a vertical line is considered to be undefined.
The slope of a vertical line is undefined.
More Information
Vertical lines have a consistent x-coordinate and extend infinitely in the y-direction. This unique property is why their slope cannot be quantified within the standard framework of slope equations.
Tips
- Confusing the slope of a vertical line with a horizontal line: Vertical lines have an undefined slope, while horizontal lines have a slope of 0.
- Misapplying the slope formula by not recognizing that the x-coordinates are the same for points on a vertical line.