https://file.aiquickdraw.com/mathbot/file/1729698757775akk8klwk.jpg

The graph shows a shaded region, representing the solution set of an inequality. The boundary line, which is solid, indicates that points on the line are included in the solution. The line appears to follow the equation \( y = -x \), as it has a slope of -1 and crosses through the origin.

Since the shaded region is below the line, the inequality is likely \( y \leq -x \), indicating that any point below or on the line satisfies the inequality.

Let's check each point to determine which ones are solutions:

- **Point A: (-2, -4)**  
  Substituting into the inequality \( y \leq -x \):
  \[ -4 \leq -(-2) = 2 \]
  This is true because \(-4 \leq 2\).

- **Point B: (4, 6)**  
  Substituting into the inequality \( y \leq -x \):
  \[ 6 \leq -(4) = -4 \]
  This is false because \(6 \nleq -4\).

- **Point C: (6, 4)**  
  Substituting into the inequality \( y \leq -x \):
  \[ 4 \leq -(6) = -6 \]
  This is false because \(4 \nleq -6\).

- **Point D: (4, 0)**  
  Substituting into the inequality \( y \leq -x \):
  \[ 0 \leq -(4) = -4 \]
  This is false because \(0 \nleq -4\).

Thus, **the correct answer choices are A (-2, -4)**.

Would you like more details or have any questions about this? Here are some additional questions you might find helpful:

1. What is the slope of the line, and how does it affect the inequality?
2. How can you identify whether to use a solid or dashed line in a graph for inequalities?
3. Why does the shaded region represent the solution set for the inequality?
4. How would the graph change if the inequality were \( y > -x \)?
5. How can you solve inequalities algebraically to confirm graphical solutions?

**Tip:** Always substitute points into the inequality to verify if they are part of the solution set.

Which of the following points is a solution for the inequality that is graphed? (Select TWO correct answer choices)

Identify which points satisfy the inequality y ≤ -x based on the graph provided. This involves using coordinate geometry and linear equation principles to verify if the points fall within the solution region. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation