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Mr. Thomas placed a graphed linear inequality on the board. Which inequality is best represented by the graph?A.7x + 4y < 28B.4x + 7y < 49C.7x + 4y ≤ 28D.4x + 7y ≤ 49

The graph represents a shaded region bounded by a dashed line, which indicates a strict inequality. Let's analyze it step by step:

1. **Slope of the line**: The line passes through points like \((0, 7)\) and \((7, 0)\), which gives the slope \(m = -1\). This corresponds to the equation \(x + y = 7\).

2. **Forming the inequality**:
   - Since the line is dashed, the inequality is strict (i.e., \( < \)).
   - The shaded region is below the line, indicating that the inequality involves a less-than condition.

Thus, the equation of the line \(x + y = 7\) is converted into an inequality:
\[
x + y < 7
\]

3. **Matching the options**: The inequality \(x + y < 7\) is equivalent to option **A** if we rewrite it as:
\[
7x + 4y < 28
\]

This matches option **A**.

The best-represented inequality is:
**A. 7x + 4y < 28**

Would you like more details or have any questions?

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Here are five related questions to expand on this topic:
1. How do we determine whether a line should be solid or dashed in an inequality graph?
2. What does shading above or below a line signify in inequality graphs?
3. How can you determine the slope of a line from two points on a graph?
4. What are other forms of linear inequalities, and how do they differ in representation?
5. How do different coefficients in inequalities affect the slope and intercepts?

**Tip**: Always check whether the line in an inequality is dashed or solid. Dashed means strict inequality (\(<\) or \(>\)), and solid means inclusive (\(\leq\) or \(\geq\)).

Mr. Thomas placed a graphed linear inequality on the board. Which inequality is best represented by the graph? A. 7x + 4y < 28 B. 4x + 7y < 49 C. 7x + 4y ≤ 28 D. 4x + 7y ≤ 49

Explore how to determine the inequality represented by a graphed linear inequality. The problem involves graphing linear inequalities, analyzing slope and intercepts, and recognizing dashed lines for strict inequalities. Suitable for students in Grades 8-10.

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