https://file.aiquickdraw.com/mathbot/file/1730211185780pw6vdlgy.jpg

To determine which points are solutions for the graphed inequality, let's analyze the shaded region and the line.

1. **Identify the inequality**: The graph shows a line with a negative slope, where the region below it is shaded. This suggests an inequality where \( y \) is less than or equal to a line equation.

2. **Determine the line's equation**: The line passes through points \((0, 4)\) and \((4, 0)\), so we can find its slope:
   \[
   \text{slope} = \frac{0 - 4}{4 - 0} = -1
   \]
   Thus, the equation of the line is \( y = -x + 4 \).

3. **Write the inequality**: Since the shaded region is below the line, the inequality representing this region is:
   \[
   y \leq -x + 4
   \]

4. **Check each point**: Substitute each point into the inequality \( y \leq -x + 4 \) to determine if it lies within the solution region.

   - **A. (4, 6)**: \( 6 \leq -4 + 4 \Rightarrow 6 \leq 0 \) (False)
   - **B. (-4, 7)**: \( 7 \leq 4 + 4 \Rightarrow 7 \leq 8 \) (True)
   - **C. (-2, -4)**: \( -4 \leq 2 + 4 \Rightarrow -4 \leq 6 \) (True)
   - **D. (6, 4)**: \( 4 \leq -6 + 4 \Rightarrow 4 \leq -2 \) (False)
   - **E. (4, 0)**: \( 0 \leq -4 + 4 \Rightarrow 0 \leq 0 \) (True)
   - **F. (6, -1)**: \( -1 \leq -6 + 4 \Rightarrow -1 \leq -2 \) (False)

5. **Conclusion**: The points that satisfy the inequality are **B. (-4, 7)** and **C. (-2, -4)**.

Would you like further details or have questions about this solution?

---

Here are 5 related questions for further understanding:

1. How do you determine the equation of a line given two points?
2. What steps are involved in graphing an inequality on a coordinate plane?
3. Why is it important to identify the shaded region in an inequality graph?
4. How can you confirm if a point satisfies an inequality?
5. How does changing the inequality sign affect the shaded region?

**Tip**: Always start by identifying whether the shading represents "greater than" or "less than" when solving inequalities on graphs.

An inequality is graphed on the coordinate plane. Which of the following points is a solution for the inequality that is graphed? Select TWO correct answer choices.

Learn how to determine solutions for a graphed inequality on a coordinate plane. This problem explores identifying the inequality, finding the line equation, and checking point solutions. Ideal 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