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.
Answer
The equation for a vertical line is $x = a$.
Answer for screen readers
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
- 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.
- 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.
- 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.
More Information
This type of line represents situations where all points are aligned vertically. Vertical lines are important in geometry and help in defining the x-axis in Cartesian coordinates.
Tips
- 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.
