Planes parallel to Coordinate Planes

A plane in space can be described by the equation A₁x + A₂y + A₃z = D.

If two of A_i = 0, we get a plane that is parallel to coordinate plane. What is coordinate plane? Coordinate plane is a plane containing two axes, for example xy-plane is a coordinate plane containing x- and y-axis. As such, there are 3 coordinate planes in space:

1. x = 0 : this is yz-plane (the blue plane).
2. y = 0 : this is xz-plane (the purple plane).
3. z = 0 : this is xy-plane (the brown plane).

Equations like x = 1, x = -2 are planes parallel to yz-plane. 

To sketch a plane that is parallel to coordinate plane, just use 2 pairs of lines that are parallel to the respective axes. For example, to sketch the plane x = 1 (parallel to yz-plane), draw two lines that are parallel y-axis and another 2 lines parallel to z-axis. Then, just label the x-intercept. You may refer to the video below to learn the drawing of plane.

You may also slide the slider at the left column to see the movement of the plane at the right. Take note that the x/y/z-intercept changes as the plane moves. You may also choose to play around with the planes here.

Betty, Created with GeoGebra, Screencast-O-Matic and Thomas Calculus, Pearson.