Question

which is the graph of $2x + 3y > -3$?

Explanation:

Step1: Rewrite to slope-intercept form

Start with the inequality $2x + 3y > -3$. Isolate $y$:

$$\begin{align*} 3y &> -2x - 3 \\ y &> -\frac{2}{3}x - 1 \end{align*}$$

Step2: Identify line properties

The boundary line is $y = -\frac{2}{3}x - 1$, which has a slope of $-\frac{2}{3}$ and y-intercept at $(0, -1)$. Since the inequality is $>$, the boundary line is dashed.

Step3: Determine shaded region

Test the origin $(0,0)$ in the inequality: $0 > -\frac{2}{3}(0) - 1$ simplifies to $0 > -1$, which is true. So the region containing the origin (above the line) is shaded.

Step4: Match to graph

The line with slope $-\frac{2}{3}$, dashed, and shaded above (including the origin) is the fourth graph (rightmost option).

Answer:

The rightmost graph (dashed line $y = -\frac{2}{3}x - 1$ with shading above the line)