identifying the graph of an inequality\nwhich is the graph of 2x + 3y > - 3?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, solve $2x + 3y>-3$ for $y$. Subtract $2x$ from both sides: $3y>-2x - 3$. Then divide by 3: $y>-\frac{2}{3}x - 1$.

Step2: Analyze the boundary line

The boundary line of the inequality $y>-\frac{2}{3}x - 1$ is the equation $y =-\frac{2}{3}x - 1$. Since the inequality is $y>-\frac{2}{3}x - 1$ (not $y\geq-\frac{2}{3}x - 1$), the boundary line is dashed.

Step3: Test a point

We can test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the original inequality $2x+3y>-3$. We get $2(0)+3(0)=0>-3$, which is true. So the region that contains the point $(0,0)$ is the solution region.

The graph of the inequality $y>-\frac{2}{3}x - 1$ has a dashed line with a slope of $-\frac{2}{3}$ and a $y$-intercept of - 1, and the region above the line (including the region containing the origin) is shaded. Without seeing the specific details of the given graphs, the correct graph is the one with a dashed line $y =-\frac{2}{3}x - 1$ and the region above the line shaded.