What surface is represented by the equation z=3 ?
The surface represented by z = 3 is a plane consisting of all point that have the z co-ordinate as 3.
The x and y co-ordinates can take on any value.
The only constraint we have here is that all points that form the plane have the z-coordinate as 3.
The surface represented by z = 3 consists of all points that have the value of the z-coordinate as 3.
In general, an equation x = k, represents a plane, parallel to y-z plane.
The equation y = k, represents a plane, parallel to x-z plane.
The equation z = k, represents a plane, parallel to x-y plane.
The equation z = 3 represents the set of all points whose z coordinate is 3.
Therefore, the equation z = 3 is the horizontal plane, that is parallel to x-y plane and it is located 3 units above x-y plane.