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

To determine the inequality represented by the graph Mr. Thomas put on the board, here are the general steps to analyze:

1. **Identify the Boundary Line**: The inequality's boundary line can be found by turning the inequality into an equation. For example, if we suspect the inequality is \(7x + 4y \leq 28\), we start by considering the equation \(7x + 4y = 28\).

2. **Check the Slope and Y-intercept**: From the boundary line equation, put it in slope-intercept form (\(y = mx + b\)) to observe the slope and intercept. This helps us see if the line matches the graph.

3. **Analyze the Inequality Symbol**:
   - If the graph has a **solid line**, it represents \(\leq\) or \(\geq\).
   - If the line is **dashed**, it represents \(<\) or \(>\).

4. **Check the Shaded Area**: The shaded region indicates which side of the line the inequality covers. For example, if shading is below the line, we expect \(y \leq\) (or \(<\)) form.

Let's apply these steps to the answer choices:

- **Option A**: \(7x + 4y < 28\)
- **Option B**: \(4x + 7y < 49\)
- **Option C**: \(7x + 4y \leq 28\)
- **Option D**: \(4x + 7y \leq 49\)

Since the answer depends on the line's characteristics and shaded region, we need to match it with these properties in the graph. 

Could you provide details on whether the line is solid or dashed and the shaded region's location relative to the line?

Which inequality is best represented by the graph?
A. 7x + 4y < 28
B. 4x + 7y < 49
C. 7x + 4y ≤ 28
D. 4x + 7y ≤ 49

Learn how to identify the best inequality represented by a graphed linear inequality. This problem involves interpreting graphing characteristics such as boundary lines, shading, and inequality symbols, tailored for students in Grades 8-10.

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