https://file.aiquickdraw.com/mathbot/file/1726615516141k61vwlb1.jpg

The image presents a problem involving a linear inequality and a question about determining whether a point lies within a shaded region.

The inequality shown is:
\[
y \geq -2x + 3
\]
The problem asks if the point \((-2, 4)\) satisfies this inequality.

### Steps to Solve:

1. **Substitute** the coordinates of the point \((-2, 4)\) into the inequality to check if it's a solution:
   - The inequality is \(y \geq -2x + 3\).
   - For the point \((-2, 4)\), \(x = -2\) and \(y = 4\).

2. **Substitute into the equation**:
   \[
   4 \geq -2(-2) + 3
   \]
   Simplifying the right-hand side:
   \[
   4 \geq 4 + 3
   \]
   \[
   4 \geq 7
   \]

3. **Conclusion**: The inequality \(4 \geq 7\) is false. Therefore, the point \((-2, 4)\) does **not** satisfy the inequality.

In the sketch provided, it appears there's a graph of the inequality, with shading showing the region that satisfies the inequality. The point \((-2, 4)\) falls outside the shaded region, confirming that it is not a solution.

Would you like further details on solving inequalities or graphing them? Here are a few follow-up questions for practice:

1. How do you graph a linear inequality like \(y \geq -2x + 3\)?
2. What changes when the inequality symbol is \(>\) instead of \( \geq\)?
3. What does the boundary line represent in the context of an inequality?
4. How do you determine the shaded region in an inequality graph?
5. Can a point lie exactly on the boundary line and still satisfy the inequality?

**Tip**: When graphing linear inequalities, the boundary line is solid for \( \geq \) or \( \leq \) and dashed for \( > \) or \( < \).

Determine if the point (-2, 4) is the solution of the inequality y ≥ -2x + 3.

This problem involves determining if the point (-2, 4) satisfies the inequality y ≥ -2x + 3. Learn how to check the solution using substitution and graphical methods, including step-by-step explanations. Suitable for Grades 8-10.

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