You can easily graph equations in three dimensions using the x-intercept, the y-intercept, and the z-intercept. The graph of an equation in two dimensions is a line. However, the graph of an equation in three dimension is a plane as shown below.
For example, when the coordinate plane xy intersects the graph of a plane, the line of intersection is called xy-trace.
1. Find all three intercepts
2. Draw all three traces
3. Show the plane with shading
Sketch the graph of 3x + 2y + 4z = 12
Find the three intercepts.
To find the x-intercept, substitute 0 for y and z.
3x + 2y + 4z = 12
3x + 2(0) + 4(0) = 12
3x = 12
x = 4
To find the y-intercept, substitute 0 for x and z.
3(0) + 2y + 4(0) = 12
2y = 12
y = 6
To find the z-intercept, substitute 0 for x and y.
3(0) + 2(0) + 4z = 12
4z = 12
z = 3
Draw all three traces and show the plane with shading.