Chapter 13.4, Problem 1PSA

(a)

To determine

To plot: The graph of given inequality.

Answer to Problem 1PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $2x-3y<6$ .

Graph is described as:

  $\begin{array}{c}2x-3y<6\\ 2\left(0\right)-3\left(0\right)<6\\ 0<6\left[\text{true}\right]\end{array}$

The graph is shaded above.

The table for the line graph $2x-3y=6$ is given as:

$x$	$0$	$3$
$y$	$-2$	$0$

The graph is given as:

  

Therefore, the graph is shown above.

(b)

To determine

To plot: The graph of given inequality.

Answer to Problem 1PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $y<\frac{1}{2}x-1$ .

Graph is described as:

  $\begin{array}{c}y<\frac{1}{2}x-1\\ 0<\frac{1}{2}\left(0\right)-1\\ 0<-1\left[\text{false}\right]\end{array}$

The graph is shaded below the graph line.

The table for the line graph $y=\frac{1}{2}x-1$ is given as:

$x$	$0$	$2$
$y$	$-1$	$0$

The graph is given as:

  

Therefore, the graph is shown above.

(c)

To determine

To plot: The graph of given inequality.

Answer to Problem 1PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $5x+2y\ge 10$ .

Graph is described as:

  $\begin{array}{c}5x+2y\ge 10\\ 5\left(0\right)+2\left(0\right)\ge 10\\ 0\ge 10\left[\text{false}\right]\end{array}$

The graph is shaded right to the graph line.

The table for the line graph $5x+2y=10$ is given as:

$x$	$0$	$2$
$y$	$5$	$0$

The graph is given as:

  

Therefore, the graph is shown above.

(d)

To determine

To plot: The graph of given inequality.

Answer to Problem 1PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $x<-2$ .

Graph is described as:

  $\begin{array}{c}x<-2\\ 0<-2\left[\text{false}\right]\end{array}$

The graph is shaded left to the graph line.

The table for the line graph $x=-2$ is given as:

$x$	$-2$	$-2$
$y$	$0$	$3$

The graph is given as:

  

Therefore, the graph is shown above.

(e)

To determine

To plot: The graph of given inequality.

Answer to Problem 1PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $y\ge 2x+3$ .

Graph is described as:

  $\begin{array}{c}y\ge 2x+3\\ 0\ge 2\left(0\right)+3\left[\text{false}\right]\end{array}$

The graph is shaded to the left.

The table for the line graph $y=2x+3$ is given as:

$x$	$0$	$-1.5$
$y$	$3$	$0$

The graph is given as:

  

Therefore, the graph is shown above.