## Answer :

1.

**Rewrite the Inequality**:

To put the equation in a more familiar form, we need to isolate [tex]\( y \)[/tex].

[tex]\[ y + 2 > -3x - 3 \][/tex]

Subtract 2 from both sides:

[tex]\[ y > -3x - 3 - 2 \][/tex]

Simplify the right-hand side:

[tex]\[ y > -3x - 5 \][/tex]

2.

**Identify the Line**:

The inequality [tex]\( y > -3x - 5 \)[/tex] involves a linear expression on the right-hand side. To graph this inequality, first, consider the related equation where the inequality is replaced by an equality:

[tex]\[ y = -3x - 5 \][/tex]

3.

**Graph the Line [tex]\( y = -3x - 5 \)[/tex]**:

- This line has a slope of [tex]\(-3\)[/tex] and a y-intercept of [tex]\(-5\)[/tex].

- To graph it, start at [tex]\((0, -5)\)[/tex] on the y-axis.

- From the y-intercept, use the slope to find another point. A slope of [tex]\(-3\)[/tex] means that for every 1 unit you move to the right (positive x-direction), you move 3 units down (negative y-direction). So starting from [tex]\((0, -5)\)[/tex], moving to the point [tex]\((1, -8)\)[/tex] (since [tex]\(-5 - 3 = -8\)[/tex]) gives another point on the line.

4.

**Draw the Line**:

Since the inequality is strict ([tex]\(>\)[/tex]), we use a dashed line to represent the boundary where [tex]\( y = -3x - 5 \)[/tex]. A dashed line indicates that points on the line are not included in the solution set.

5.

**Shade the Appropriate Region**:

The inequality is [tex]\( y > -3x - 5 \)[/tex]. This means that we shade the region above the line. Any point in this region will have a y-coordinate greater than [tex]\(-3x - 5\)[/tex].

6.

**Conclusion**:

The graph should show:

- A dashed line representing [tex]\( y = -3x - 5 \)[/tex].

- The area above this line should be shaded.

So, the characteristics of the graph we derived are:

- The slope of the line is [tex]\(-3\)[/tex].

- The y-intercept of the line is [tex]\(-5\)[/tex].

- The inequality is strict ([tex]\(>\)[/tex]), meaning the line is dashed.

- The shaded region is above the line.

These characteristics match the results:

[tex]\[ (-3, -5, '>', 'dashed') \][/tex]

This detailed explanation should help you correctly draw and understand the graph of the inequality [tex]\( y + 2 > -3x - 3 \)[/tex].