The problem asks us to graph the inequality $5x + 2y > -4$.

1. Problem Description

The problem asks us to graph the inequality $5x + 2y > -4$.

2. Solution Steps

First, we need to rewrite the inequality in slope-intercept form, which is $y = mx + b$. To do this, we isolate $y$:

$5x + 2y > -4$

$2y > -5x - 4$

$y > -\frac{5}{2}x - 2$

Now, we can identify the slope $m$ and the y-intercept $b$.

$m = -\frac{5}{2}$

$b = -2$

The y-intercept is at the point $(0, -2)$. We use the slope $-\frac{5}{2}$ to find another point on the line. Starting from $(0, -2)$, we go down 5 units and right 2 units to reach $(2, -7)$. The slope can also be seen as $\frac{5}{-2}$, meaning we go up 5 and left 2 units, and get $(-2, 3)$.

We draw a dashed line through these points because the inequality is strict ($>$ and not $\geq$).

Since $y$ must be greater than $-\frac{5}{2}x - 2$, we shade the region above the line.

3. Final Answer

The solution is the graph of the dashed line $y = -\frac{5}{2}x - 2$, with the region above the line shaded.