If we are tracing X-Y plane, then Set Z to zero. If we want to trace Y-Z plane, then set X to zero and to trace X-Z plane, Y will be set to zero.
If in the given equation, plane does not have a variable, then plane will be parallel to that axis which is expressed by missing variable.
Let us consider an equation to understand how to graph in xyz plane. x, y and z are the cartesian coordinates.
x - 2y + 3z = 6
For this equation, lets draw x-y, y-z and x-z planes and plot graph for these planes using the equation.
First of all, trace x-y plane and draw the graph for x-y plane using the equation x - 2y = 6 which is a line equation. When y = 0, then x = 6 and when x = 0, y = -3. Using these values, we draw the graph which will look as shown below:
Now, consider the line equation -2y + 3z = 6 to plot the graph for yz plane. When z = 0, y = - 3 and when y = 0, z = 2. Let us use these values and draw the graph which looks as follows:
Now, to trace the graph for the x z plane, we use x + 3z = 6 as line equation and on substituting x and z to zero, we get z = 2 and x = 6. Plot the graph using these values. it will look as
Now finally, using these three equations and the three graphs, we can draw the graph for x - 2y + 3z = 6. This will be drawn as follows:
The shaded area in the above graph shows that this graph exists in all three planes.