Final answer:
The equation y=3 in three-dimensional space represents a plane that is parallel to the x-z plane and remains 3 units above it, extending infinitely along the x and z axes.
Step-by-step explanation:
The equation y=3 in three-dimensional space describes a plane that is parallel to the x-z plane. To visualize this, you can think of the standard right-handed Cartesian coordinate system, where we have three orthogonal axes labeled x, y, and z. In this system, a point is defined by its coordinates (x, y, z).
If we fix the y-coordinate of every point in this space to be 3, regardless of the x and z values, we end up with a flat surface that doesn't vary in height as we move along the x or z directions. Since the equation does not involve x or z, any value for x and z will satisfy the equation as long as y is always 3. This results in a plane extending infinitely along the x-axis and z-axis but remaining constantly 3 units above the x-z plane. Essentially, every point on this plane has the same y-value, which is 3, and can vary freely in the x and z directions, making the shape a flat plane.