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

Question
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
image
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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