🎧 New: AI-Generated Podcasts Turn your study notes into engaging audio conversations. Learn more

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

  1. 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.

  1. 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.

  1. 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.

  1. 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.
Thank you for voting!
Use Quizgecko on...
Browser
Browser