Question

Find the intercepts and sketch the graph of the plane. $$ z=8 $$

Short answer

The Z intercept of the plane \(z = 8\) is at z=8. The plane does not have X and Y intercepts since it is parallel to the X-Y plane. The graph of the plane reveals a line parallel to the x-y plane, passing through the point (0,0,8).

Step-by-step solution

Define the plane equation

The equation of the plane is given by \(z = 8\). This plane is parallel to the x-y plane and intersects the z-axis at 8 units.

Find X and Y intercepts

The plane is parallel to X-Y plane, meaning it doesn't intersect the X and Y axes. Hence, there would be no X and Y intercepts.

Find Z intercept

The Z intercept is found where the plane intersects the Z-axis. For the given plane, the Z intercept is at z=8.

Sketch the graph of the plane

The graph will be a plane parallel to the x-y plane and passing through the point (0,0,8). It can be implemented by drawing an x-y graph, and a line parallel to the x-y plane which indicates z=8. The point where this line is present would be the z-intercept and the position of the plane.