https://file.aiquickdraw.com/mathbot/file/17266741142416zu2dn2z.jpg

The problem asks you to graph the solution set of the linear inequality:

\[
x + y < -1
\]

### Steps to Graph the Inequality:

1. **Rewrite the inequality**: We first rewrite the inequality in slope-intercept form:
   \[
   y < -x - 1
   \]
   This form is useful for graphing since it tells us the slope and the y-intercept.

2. **Graph the boundary line**:
   - The boundary line is given by the equation \( y = -x - 1 \), where the slope is -1 and the y-intercept is -1.
   - To graph this line:
     - Start at the point (0, -1) on the y-axis.
     - Use the slope (-1) to find another point by going down 1 unit and to the right 1 unit. Plot a second point at (1, -2).
   - Since the inequality is **strict** (i.e., \( y < \) and not \( \leq \)), the boundary line should be **dashed**, meaning the points on the line are not included in the solution set.

3. **Shading the region**:
   - To determine which side of the line to shade, we can test a point not on the boundary line. The origin (0, 0) is an easy choice.
   - Plug (0, 0) into the inequality:
     \[
     0 + 0 < -1 \quad \text{(False)}
     \]
     Since the origin does not satisfy the inequality, we shade the side **below** the line, where the inequality holds true.

The shaded region represents all the points where \( x + y < -1 \), which is the solution set to the inequality.

Would you like more details on how to graph or any further questions on this topic? Here are a few related questions for practice:

1. How would the graph change if the inequality was \( x + y \leq -1 \)?
2. What would the graph look like if the inequality was \( y > -x - 1 \)?
3. Can you describe the solution set in terms of regions in the coordinate plane?
4. What would be the slope and y-intercept for the inequality \( x + 2y < 4 \)?
5. How do you check if a point is part of the solution set of a linear inequality?

**Tip**: When graphing inequalities, always remember that a **dashed line** indicates that points on the line are not included in the solution, while a **solid line** indicates that points on the line are part of the solution.

Graph the solution set of the linear inequality x + y < -1.

Learn how to graph the linear inequality x + y < -1. This problem involves understanding linear equations, slope-intercept form, and identifying solution regions using graphing. Suitable for students in Grades 7-10.

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