6.3.2: Graphing Vertical and Horizontal Lines

Learning Objectives

Type your learning objectives here.

Graph a vertical line
Give the equation of a vertical line
Graph a horizontal line
Give the equation of a horizontal line

Key words

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vertical line: a line that runs in the same direction as the $y$ -axis
horizontal line: a line that runs in the same direction as the $x$ -axis

Vertical and Horizontal Lines

Consider the vertical line graphed in figure 1, and the solution table that goes with it.

x=2

$x$	$y$
2	-3
2	-1
2	0
2	1
2	3

No matter the value of $y$ , $x=2$ . So $x=2$ is the equation of the line.

Figure 1.

VERTICAL LINES

The equation of a vertical line is given as: $x=c$ where c is a constant.

To graph the equation on the coordinate plane, we need both $x$ and $y$ variables in the equation. Therefore, the equation of the vertical line in two variables is: $x+0y=c$ where c is a constant.

Consider the horizontal line graphed in figure 2, and the solution table that goes with it.

y=3

$x$	$y$
-3	3
-1	3
0	3
2	3
4	3

No matter the $x$ -value, the $y$ -value is always 3. So the equation of the line is $y=3$ .

Figure 2.

HORIZONTAL LINES

The equation of a horizontal line is given as: $y=c$ where c is a constant.

To graph the equation on the coordinate plane, we need both $x$ and $y$ variables in the equation. Therefore, the equation of the horizontal line in two variables is $0x+y=c$ .

Suppose we want to graph a the lines with equations $x+0y=-3$ and $0x+y=-2$ .

The following points satisfy the first equation: $\left(-3,-5\right),\left(-3,1\right),\left(-3,3\right)$ , and $\left(-3,5\right)$ . We can plot the points. Notice that all of the $x$ –coordinates are the same and we find a vertical line through $x=-3$ .

The following points satisfy the second equation: $\left(-2,-2\right),\left(0,-2\right),\left(3,-2\right)$ , and $\left(5,-2\right)$ . The graph is a horizontal line through $y=-2$ . Notice that all of the $y$ –coordinates are the same.

Coordinate plane with the x-axis ranging from negative 7 to 4 and the y-axis ranging from negative 4 to 4. The function y = negative 2 and the line x = negative 3 are plotted. x = −3 is a vertical line.
y = −2 is a horizontal line.

try it

Use an online graphing tool to graph the following:

A horizontal line that passes through the point (-5,2)
A vertical line that passes through the point (3,3)

Example

Find the equation of the line passing through the given points: $\left(1,-3\right)$ and $\left(1,4\right)$ .

Solution

The $x$ –coordinate of both points is 1. Therefore, we have a vertical line: $x=1$ .

Try It

Find the equation of the line passing through $\left(-5,2\right)$ and $\left(2,2\right)$ .

Show Answer

Horizontal line: $y=2$

Chapter 6: Linear Equations in Two Variables