A vertical line is a straight line that goes up and down and has an undefined slope. It is represented by an equation of the form $x = a$, where $a$ is a constant.
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A vertical line has no y-intercept because it does not cross the y-axis.
The slope of a vertical line is undefined.
Vertical lines are used to test for functions using the Vertical Line Test. If any vertical line intersects a graph more than once, the graph is not a function.
In the equation $x = a$, 'a' represents the x-coordinate where the vertical line crosses the x-axis.
Vertical lines are perpendicular to horizontal lines, which have zero slope.
Review Questions
What is the slope of a vertical line?
How would you write the equation of a vertical line that passes through the point (3, -2)?
Why can't a vertical line be used as a function in terms of input-output pairs?
Related terms
Slope: Slope measures the steepness of a line and is calculated as rise over run. For non-vertical lines, it is represented as $m$ in linear equations.
Horizontal Line: A horizontal line runs left to right and has zero slope. Its equation is written as $y = b$, where $b$ is a constant.
Vertical Line Test: A method used to determine if a graph represents a function by checking if any vertical line intersects the graph more than once.