Chapter 6.5, Problem 5P

Graph each linear inequality.

$3x+2y>6$

To determine

To graph: $3x+2y>6$

Explanation of Solution

Given information: $3x+2y>6$

Graph:

  Interpretation: The boundary of the graph is the graph of $3x+2y=6$ . Since, the inequality symbol is >, the boundary is dashed.

The point $(0,0)$ has to be checked as it is not on the boundary line.

  $\begin{array}{l}3x+2y>6\\ \Rightarrow 3(0)+2(0)>6\\ \Rightarrow 0>6\end{array}$

Since, the statement is false, the region that does not contain $(0,0)$ is shaded.

The shaded region is the graph of the inequality $3x+2y>6$ .