Question

Surfaces in Three Dimensions Describe and sketch the surface represented by the given equation.

$y=-1$.

Short answer

The equation $y=-1$ represents thezcoordinate of the$xyz$plane. The surface that is represented by the equation $y=-1$, is the vertical plane that is parallel to thexz plane and -1 units right of it. It is given by,

Step-by-step solution

Step 1. Given information.

Given: $y=-1$

Step 2. Finding x,z coordinate values.

The surface in three-dimensional space can be made up of the points P$(x,y,z)$. So, the given equation$y=-1$,represents the coordinate of the point $P$ . From this, we can found that the coordinates of xandz are zero.

Plot the point $(0,-1,0)$ in the $xyz$ plane, we get

Step 3. Sketch the surface that is represented by the equation y=-1.

In the graph, the surface that is represented by the equation $y=-1$, is the vertical plane that is parallel to thexz plane and -1 units left of it.