Monica graphed the boundary lines for a system of linear inequalities.
 

 
If Monica shaded the area with point B
, what will be the system of linear inequalities?
 
Move the correct answer to each box. Not all answers will be used.
 
y
    x − 8

y
    x + 2

To determine the system of linear inequalities based on Monica's shaded area that includes point B, we need to interpret the inequalities based on the position of point B relative to the boundary lines on the graph.

For a precise solution, I would need a few details:
- The slopes and y-intercepts of the boundary lines,
- The location of point B relative to these lines,
- If possible, an image of the graph.

The options you provided:
1. \( y < x - 8 \)
2. \( y \leq x - 8 \)
3. \( y > x - 8 \)
4. \( y \geq x - 8 \)
5. \( y < x + 2 \)
6. \( y \leq x + 2 \)
7. \( y > x + 2 \)
8. \( y \geq x + 2 \)

Each option suggests a comparison to a line with the form \( y = x - 8 \) or \( y = x + 2 \). We would select inequalities based on the side of the line where point B is located and whether the boundary line is included or not (indicated by \( \leq \) or \( \geq \)).

If you can provide any additional details or upload the graph, I can help you select the correct inequalities. 

Would you like more information on solving inequalities? Here are some follow-up questions:
1. What does it mean when we shade below or above a line in an inequality?
2. How can we test a point to see if it satisfies an inequality?
3. How does changing the inequality symbol (e.g., \( < \) to \( \leq \)) affect the shaded region?
4. What role does the slope play in determining the direction of the inequality?
5. How can we confirm the correct inequalities for a system graphically?

**Tip:** To determine if a point is part of a solution to an inequality, substitute its coordinates into the inequality. If the statement is true, the point satisfies the inequality.

Monica graphed the boundary lines for a system of linear inequalities. If Monica shaded the area with point B, what will be the system of linear inequalities? Move the correct answer to each box. Not all answers will be used. y = x - 8, y = x + 2

Learn to determine the system of linear inequalities for a shaded region on a graph with boundary lines. Explore concepts in graphing inequalities, interpreting slopes, and using points to identify correct inequalities. Suitable for students in Grades 8-10.

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