What if you were given the graph of a vertical or horizontal line? How could you write the equation of this line? After completing this Concept, you'll be able to write horizontal and vertical linear equations and graph them in the coordinate plane.
Watch This
CK12 Foundation: 0404S Graphs of Horizontal and Vertical Lines (H264)
Guidance
How do you graph equations of horizontal and vertical lines? See how in the example below.
Example A
“Madcabs” have an unusual offer going on. They are charging $7.50 for a taxi ride of any length within the city limits. Graph the function that relates the cost of hiring the taxi
To proceed, the first thing we need is an equation. You can see from the problem that the cost of a journey doesn’t depend on the length of the journey. It should come as no surprise that the equation then, does not have
The graph of this function is shown below. You can see that it’s simply a horizontal line.
Any time you see an equation of the form “
Similarly, when you see an equation of the form
Example B
Plot the following graphs.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Example C
Find an equation for the
Look at the axes on any of the graphs from previous examples. We have already said that they intersect at the origin (the point where
So using example 3 as our guide, we could define the
Watch this video for help with the Examples above.
CK12 Foundation: Graphs of Horizontal and Vertical Lines
Vocabulary

Horizontal lines are defined by the equation
y= constant and vertical lines are defined by the equationx= constant.  Be aware that although we graph the function as a line to make it easier to interpret, the function may actually be discrete.
Guided Practice
Write the equation of the horizontal line that is 3 units below the xaxis.
Solution:
The horizontal line that is 3 units below the xaxis will intercept the yaxis at
Practice
 Write the equations for the five lines (
A throughE ) plotted in the graph below.
For 210, use the graph above to determine at what points the following lines intersect.

A andE 
A andD 
C andD 
B and the \begin{align*}y\end{align*}axis  \begin{align*}E\end{align*} and the \begin{align*}x\end{align*}axis
 \begin{align*}C\end{align*} and the line \begin{align*}y = x\end{align*}
 \begin{align*}E\end{align*} and the line \begin{align*}y = \frac {1} {2} x\end{align*}
 \begin{align*}A\end{align*} and the line \begin{align*}y = x + 3\end{align*}
 \begin{align*}B\end{align*} and the line \begin{align*}y=2x\end{align*}