What is the definition of a Vertical Line?
Vertical lines can be found in our daily lives in the form of steel fence rails, tall trees standing upright, table legs, and so on. Let’s learn more about such lines.
A vertical line is a line parallel to the Y-axis in a coordinate plane. The x-coordinate for any point along this line will be the same. The coordinate points of vertical lines are, for example, represented as (5, 0), (1, 0), (- 4, 0), and so on.
A horizontal line, on the other hand, is a line that runs from left to right, or, right to left and is parallel to the x-axis.
Vertical Line Equation
Vertical lines run parallel to the y-axis, so their slope isn’t defined. As a result, the equation of the vertical line crossing the x-axis at any point ‘a’ is:
x = a
Where, x is the coordinate of a point on the line and a is the point at which the line crosses the x-intercept. The difference between vertical and horizontal lines is illustrated in the image below.
The left side of the above diagram depicts vertical lines in a coordinate plane, while the right side depicts horizontal lines parallel to the x-axis.
Properties of Vertical Line
- The vertical line is parallel to the y-axis, the vertical line’s equation does not have a y-intercept.
- A vertical line’s equation is always written as x = a, with a denotes the x-intercept.
- A vertical line’s slope is undefined. The denominator of the slope is zero because the x-coordinates do not change.
- In math, the vertical line is used to determine whether a relation is a function.
Solved Vertical Line Examples
Example 1: If Alison travels along a straight line that is denoted by the equation x = 6. Then create a graph to display this.
Solution:
x = 6 is a vertical line parallel to the y-axis that passes through the x-axis at a distance of 6 units to the right of the origin.
Example 2: In the graph below, find the equation for the vertical line.
Solution:
We need to figure out what the coordinates are in the graph.
The coordinates of the point are (– 4, 1).
As a result, the equation of the vertical line is:
x = – 4 or x + 4 = 0
Example 3: What is the slope of a line with equation x = – 7?
Solution:
A vertical line is represented by the equation x = – a.
The slope of a vertical line is undefined, as we all know.
Hence, the vertical line x = – 7 has an undefined slope.
A vertical line is a line on the coordinate plane with the same x-coordinate for any value of the y-coordinate.
In a vertical line the x-coordinates are the same, and the slope of a vertical line is undefined. This is because there is no change in the x-coordinates, the denominator in the slope calculation becomes zero.
In a coordinate plane, a vertical line runs straight from top to bottom and from bottom to top.
x = – 2 is a vertical line that passes through the x-axis and is parallel to the y-axis. It is 2 units to the left of the origin.
A vertical line that passes through the origin and is parallel to the y-axis is known as x = 0.