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# Descibe in words the region of RR^{3} represented by the equation or inequality.y = -2 # Descibe in words the region of RR^{3} represented by the equation or inequality.y = -2

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Alternate coordinate systems asked 2021-03-02

Descibe in words the region of $$\mathbb{R^{3}}$$ represented by the equation or inequality.
$$y = -2$$

## Answers (1) 2021-03-03

The equation $$y = -2\ in\ \mathbb{R^{3}}$$ represenrs the vertical plane that is parallel to the xz - plane and it locates 2 units left to the xz - plane.
$$RR^{3}$$ is the three dimensional coordinate system which contains x, y and z - coordinates.
The equation $$y = -2\ in\ \mathbb{R^{3}}$$
represents the set $${(x, y, z)|y = -2}$$,
which is the set of all points in $$\mathbb{R^{3}}$$ whose y - coordinate is -2 and x, z - coordinates are any values.
The equation $$y = -2\ in\ \mathbb{R^{3}}$$ is sketched as shown in Figure 1 From Figure 1, the equation $$y = -2\ in\ \mathbb{R^{3}}$$ represents the vertical plane that is parallel to the xz - plane and it locates 2 units left to the xz - plane.
Thus, the equation $$y = -2\ in\ \mathbb{R^{3}}$$ is described.

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