Question

Sketch graphs of the equations in 3 -space. $$y=1$$

   Sketch graphs of the equations in 3 -space.
$$y=1$$

Calculus Multivariable

Calculus Multivariable

Deborah… 7th Edition

Chapter 12, Problem 14

Instant Answer

Solved by Expert Kayla Robinson

07/02/2021

Step 1

This equation implies that the y-coordinate of all points on the graph is fixed at the value 1. This means that the graph will look like an xz-plane shifted up along the positive y-axis by one unit. Show more…

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Sketch graphs of the equations in 3 -space. $$y=1$$

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Key Concepts

Graphing in Three-Dimensional Space

Graphing in three-dimensional space involves visualizing and sketching surfaces or curves based on equations in a 3D coordinate system. When graphing an equation like y = 1, it is important to recognize that it defines a flat, two-dimensional plane that is parallel to the xz-plane. Understanding this concept aids in correctly interpreting the spatial properties and orientation of the geometric object represented by the equation.

Cartesian Coordinate System

The Cartesian coordinate system in three-dimensional space is defined by three perpendicular axes: x, y, and z. This coordinate system allows us to designate any point in space with an ordered triple (x, y, z), providing a framework for representing and analyzing geometric objects and their positions in a 3D environment.

Equation of a Plane

An equation like y = 1 represents a plane in three-dimensional space. This specific equation indicates that for every point on the plane, the y-coordinate is fixed at 1, while the x and z coordinates can be any real numbers. This means the plane extends infinitely in the directions of the x-axis and z-axis while maintaining a constant distance from the xz-plane.

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