Graph a horizontal or vertical line

Key notes

Introduction

In coordinate geometry, horizontal and vertical lines are special types of straight lines that are easy to graph because their equations are simple.

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Horizontal Lines

Definition:
A horizontal line runs left to right and is parallel to the x-axis.

Equation form:

y=c

where c is a constant (a fixed number).

Characteristics:

• The y-coordinate is always the same for every point on the line.
• The slope of a horizontal line is 0.

Example:
Equation: y=3
This means the line passes through all points where y = 3, such as (0,3), (2,3), (−4,3), etc.

Graphing steps:

• Draw a horizontal line passing through y = 3 on the y-axis.
• The line extends infinitely left and right.

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Vertical Lines

Definition:
A vertical line runs up and down and is parallel to the y-axis.

Equation form: x=k where k s a constant (a fixed number).

Characteristics:

• The x-coordinate is always the same for every point on the line.
• The slope of a vertical line is undefined.

Example:
Equation: x=−2
This means the line passes through all points where x = −2, such as (−2,0), (−2,5), (−2,−3), etc.

Graphing steps:

• Draw a vertical line passing through x = −2 on the x-axis.
• The line extends infinitely up and down.

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Summary Table

Type of Line	Equation	Slope	Description
Horizontal line	y=c	0	Parallel to x-axis
Vertical line	x=k	Undefined	Parallel to y-axis

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Practice Questions

1. Graph the line y=4 on the coordinate plane.
2. Graph the line x=−1 on the coordinate plane.
3. Identify if the line y=−5 is horizontal or vertical.
4. What is the slope of the line x=0?

Learn with an example

Let’s Practice!