https://file.aiquickdraw.com/mathbot/file/1730061911424v3jofu9y.jpg

To graph the inequalities in this system, we’ll first analyze each inequality separately:

1. **First inequality**: \( y < \frac{1}{2}x + 1 \)
   - This inequality represents a line with a slope of \( \frac{1}{2} \) and a y-intercept at \( (0, 1) \).
   - Since the inequality is \( y < \frac{1}{2}x + 1 \), we will use a dashed line to indicate that points on the line itself are not included.
   - We shade the region below this line because of the "<" sign.

2. **Second inequality**: \( y > -x - 2 \)
   - This inequality represents a line with a slope of \( -1 \) and a y-intercept at \( (0, -2) \).
   - Since the inequality is \( y > -x - 2 \), we use a dashed line here as well.
   - We shade the region above this line because of the ">" sign.

### Solution Steps
1. Plot the lines \( y = \frac{1}{2}x + 1 \) and \( y = -x - 2 \) using dashed lines.
2. Shade the region below the first line (representing \( y < \frac{1}{2}x + 1 \)).
3. Shade the region above the second line (representing \( y > -x - 2 \)).
4. The solution to the system is the area where the shaded regions overlap.

Would you like a step-by-step graphing explanation or have any questions?

### Related Questions
1. What is the solution set for a system of linear inequalities?
2. How do you determine which side of the line to shade for a given inequality?
3. Why are dashed lines used instead of solid lines for strict inequalities?
4. How can you verify a point is in the solution region?
5. What are real-world applications of systems of linear inequalities?

**Tip:** Always check if an inequality includes an "equal to" condition to know whether to use a dashed or solid line on the graph.

Graph the system of inequalities: y < (1/2)x + 1 and y > -x - 2.

Explore how to graph the system of linear inequalities y < (1/2)x + 1 and y > -x - 2. Learn about inequality shading, dashed lines, and overlap regions for solutions. Ideal for Grades 9-10 students looking to understand graphing of linear inequalities.

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