# Which line has an undefined slope?

#### Understand the Problem

The question is asking for a specific line that has an undefined slope, which typically refers to a vertical line. This is because a vertical line does not have a defined slope, as it would involve division by zero.

The equation for a vertical line is $x = a$.

The equation of the line with an undefined slope is of the form $x = a$, where $a$ is the x-coordinate of any point on the line.

#### Steps to Solve

1. Identify the Characteristics of a Vertical Line

A vertical line has the form $x = a$, where $a$ is a constant. This means that the x-coordinate for all points on the line is the same, while the y-coordinate can be any value.

1. Understand Undefined Slope

The slope of a line is calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$. For a vertical line, $x_1$ and $x_2$ are the same, which means $x_2 - x_1 = 0$. As division by zero is undefined, this gives the vertical line its undefined slope.

1. Express the Equation of the Vertical Line

If we want to express the equation of a vertical line through a specific point $(a, b)$, then the equation can be directly given as $x = a$, without needing to consider the value of $b$.

The equation of the line with an undefined slope is of the form $x = a$, where $a$ is the x-coordinate of any point on the line.

• Confusing vertical lines with horizontal lines: A common mistake is thinking that a vertical line is represented by $y = b$. Remember that horizontal lines have a defined slope of $0$, while vertical lines do not.