Chapter 5.6, Problem 29E

To determine

ToGraph:The inequality $5x-2y\le 6$ in a coordinate plane.

Answer to Problem 29E

The graph of the given inequality is

  

Explanation of Solution

Given:

The inequality $5x-2y\le 6$

Concept Used:

The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane.

Calculation:

Given the inequality $5x-2y\le 6$

Consider the corresponding equation $5x-2y=6$

Graphing the equation $5x-2y=6$

For $x=0$

  $\begin{array}{c}5x-2y=6\\ 5\left(0\right)-2y=6\text{ Substitute }x=0\\ 0-2y=6\\ \frac{-2y}{-2}=\frac{6}{-2}\text{ Divide both sides by }-2\end{array}$

  $y=-3$

For $y=0$

  $\begin{array}{c}5x-2y=6\\ 5x-2\left(0\right)=6\text{ Substitute }y=0\\ 5x=6\\ \frac{5x}{5}=\frac{6}{5}\text{ Divide both sides by 5}\end{array}$

  $x=\frac{6}{5}$

The points on the equation $5x-2y=6$ are

$x$	$0$	$\frac{6}{5}$
$y$	$-3$	$0$

Since, in the given inequality $5x-2y\le 6$ , the symbol is $\le$

So, plotting the graph of the equation $5x-2y=6$ using a solid line. We have,

  

Testing a point on either side of the solid line

Consider a coordinate $\left(0,0\right)$ on left side of the solid line.

Substituting the coordinate $\left(0,0\right)$ in the given inequality on both sides, we have

  $\begin{array}{c}5x-2y\le 6\\ 5\left(0\right)-2\left(0\right)\le 6\text{ Substitute }\left(0,0\right)\\ 0\le 6\text{ Which is True}\end{array}$

Thus, $\left(0,0\right)$ is the solution of the given inequality.

Shading the half-plane that contains $\left(0,0\right)$ . The graph of the given inequality is

  

Conclusion:

The graph of the given inequality is