The system of inequalities given is:

1. $y > -3x - 2$
2. $y \leq 3x - 4$

To graph this system:

Step 1: Graph the boundary lines

• The boundary line for the first inequality $y = -3x - 2$ has a slope of -3 and a y-intercept of -2. Since the inequality is $y > -3x - 2$, this will be a dashed line, and the region above the line will be shaded.

• The boundary line for the second inequality $y = 3x - 4$ has a slope of 3 and a y-intercept of -4. Since the inequality is $y \leq 3x - 4$, this will be a solid line, and the region below the line will be shaded.

Step 2: Determine the regions to shade

• For the first inequality $y > -3x - 2$, shade the region above the dashed line $y = -3x - 2$.
• For the second inequality $y \leq 3x - 4$, shade the region below the solid line $y = 3x - 4$.

Step 3: Identify the solution region

• The solution to the system of inequalities will be the overlapping region where both shaded areas from the two inequalities meet.

Would you like me to plot this graph for you or explain any step in more detail?

Here are 5 related questions to deepen your understanding:

1. How do you determine if a line should be dashed or solid when graphing inequalities?
2. What happens if the inequalities are reversed (e.g., $y \geq -3x - 2$)?
3. How does the slope of each line affect the shape of the solution region?
4. What is the significance of the intercepts in graphing these inequalities?
5. Can you explain how to check if a point lies in the solution region?

Tip: Always test a point (like the origin) in each inequality to verify the correct shaded region.