Answer
$y \gt \frac{3}{2}x -3$
Work Step by Step
The slope of the line is $\frac{3}{2}$ and the y-intercept is $-3$, so the equation of the boundary line is $y = \frac{3}{2}x -3$.
The boundary line is dashed, so the inequality symbol is either $\lt$ or $\gt$.
Assume $y \lt \frac{3}{2}x -3$ and test a point in the region to see whether it satisfies this equation. For example, test the point $(1, -1)$.
$-1 \lt \frac{3}{2}(-1) -3$
$-1 \lt \frac{-9}{2}$
This is not true. Therefore, the correct inequality is $y \gt \frac{3}{2}x -3$.
