Chapter 8.6, Problem 52E

Solution

a)

To draw: The graph of the line defined by the pair of equations.

The graph of pair of equations is shown in Figure 1.

Given information:

The pair of equations are $y=1,z=3$ .

Formula used:

The coordinate planes are the $xy$ -plane, the $xz$ -plane and the $yz$ -plane and they have equations $z=0,y=0$ and $x=0$ respectively.

Calculation:

Plot the pair of equations $y=1,z=3$ .

  

Figure 1

b)

To give: a geometric description of the line including its direction and its position relative to the coordinate frame.

The graph of the pair of equations $y=1,z=3$ is the line that is parallel to $x-$ axis and it is the intersection of planes $y=1$ and $z=3$ respectively.

Given information:

The pair of equations are $y=1,z=3$ .

Formula used:

The coordinate planes are the $xy$ -plane, the $xz$ -plane and the $yz$ -plane and they have equations $z=0,y=0$ and $x=0$ , respectively.

Calculation:

The graph of the pair of equations $y=1,z=3$ is shown in Figure 1. It can be observed from the graph that the line is parallel to $x-$ axis and it is the intersection of planes $y=1$ and $z=3$ respectively.

Therefore, it can be said that the graph of the pair of equations $y=1,z=3$ is the line that is parallel to $x-$ axis and it is the intersection of planes $y=1$ and $z=3$ respectively.