In the -plane, the graph of the solution set of the equation  is a vertical line.  This line cannot be obtained as the graph of a function, so Maple's plot command will not graph the vertical line without user intervention.  Figure 1 shows a portion of this line drawn with the plot command as a line segment.  Figure 2 draws this same line segment as the parametric curve .

Clearly, graphing a vertical line segment via the plot command requires significant user intervention and knowledge of Maple syntax.  Figure 3 provides a graph of the vertical line segment drawn as an implicit plot with the implicitplot command from the plots package.

For more information on these methods, see plot details, parametric plot, and implicit plot.

Figures 1 - 3 all require some mathematical insight on the part of the user, who must correspondingly implement some appropriate Maple construct that reflects that view of the vertical line.  Now what happens when the user naively tries to plot  interactively via the context menu?  Right-click the equation  and from the context menu, select Plots>2-D Implicit Plot>.

The result is shown in Figure 4. You can obtain the graph through the context menu as well as by using a command.  A final way to graph a vertical line is using the Plot Builder.

First, launch the Plot Builder from the Tools>Assistants menu. In the Expressions section, click the Add button, and enter .

Pressing the Accept button will enter the equation  into the Expression box and add the variable  to the Variables box.  In the Variables section, click the Add button and add the variable .  Press Accept.  Figure 5 shows the completed Specify Expressions dialog.

Press OK and then press Plot in the main Plot Builder window.  Again, you get the graph of the vertical line.

Using the Context Menu

Consider the graph of .  On the horizontal axis, the default range ( for a trigonometric graph), default tickmarks (at multiples of ) and default labels are shown.

We want to change the tickmarks and labels on the -axis to be only at whole number multiples of  One method is to modify the graph after it has been drawn by editing the axis properties for the plot.  

Click the graph to select it, then from the Plot menu choose Axes>Properties.... (You can also access this from the context menu for the plot.)  The Axis Properties box is shown in Figure 8.

Under the Horizontal Axis tab, clear the box for Let renderer choose tickmarks, and instead select Custom Spacing (1.0) and Multiply by Pi.  The modified graph is shown in Figure 9.

Using the Plot Builder

When graphing with the Plot Builder, you can also access these options.  Use the context menu to launch the Plot Builder for your expression.  Again, we use the example .

In the Plot Builder, press the Options button to access the dialog for plot options, then select the Advanced Settings option under Axes on the lower left.  In the Advanced Axis Settings dialog box, open the drop-down listing under Tickmarks for the -axis.  Select spacing(Pi, 0).

Press the Apply button and Plot.

In the previous example, a plot was created through the Plot Builder.  If you are creating many plots, this can become a tedious way to create the modifications you want.  For more efficient graphing, you can use the Plot Builder once, and extract command with all the settings you selected.

When exiting the Plot Builder, instead of returning a plot, you can opt to return the command used to create the plot.  This provides a way to learn the way to specify these options directly to the plot command.  If you intend to graph numerous similar functions with the same plot settings, this is an efficient way to do it.  

Here are the steps to create the same plot as in the previous section and then to return a command from Plot Builder:

Use the context menu to launch the Plot Builder for your expression, such as .

In the Plot Builder, press the Options button to access the dialog for plot options, then select the Advanced Settings option under Axes on the lower left.  In the Advanced Axis Settings dialog box, open the drop-down listing under Tickmarks for the -axis.  Select spacing(Pi, 0).

Press Apply and then Command.

The result obtained from choosing Command instead of Plot is shown in Figure 11.

Now, you can copy and paste this command on a new line (ensure you are in 2-D math mode when you paste it)  to create a graph.   You can modify the command to create variations.  For instance, you can graph  without having to go through the Plot Builder steps again.

Some final illustrations of graphs obtained by modifying this command.

1. Graph of  and .

2. One period of the graphs of  and  with constrained scaling.

3. Labeling every

For more information on tickmarks, including how to place one tickmark at a fixed location and then draw other tickmarks relative to that point, see plot/tickmarks.

4.  Using the Plot Builder to play with plot settings and preview the graph can be helpful with discontinuous graphs such as .  When satisfied, return the command.

After returning the command from the Plot Builder, copy into a 2-D math region and execute.

To learn more about the options shown here as well as other options accepted by the plot command, see plot/options.

 plot, plot/options, plot/parametric, plot/tickmarks,  plots[implicitplot], plottools[line], trig