Alexander graphed a linear inequality on the coordinate plane.

Which inequality is best represented by the graph?
A.y > 32x −3

B.y < 23x −3

C.y > 23x −3

D.y < 32x −3

To determine which inequality is best represented, let's analyze each option's key components:

1. **Inequality Sign**: 
   - **“>”** (greater than) indicates that the shaded region should be **above** the line.
   - **“<”** (less than) indicates that the shaded region should be **below** the line.

2. **Slope and Intercept**: 
   - **32x** and **23x** represent the slope, showing the line’s steepness.
   - The **−3** in each inequality is the y-intercept, where the line crosses the y-axis.

### Solution Steps

1. **Determine if the shaded region is above or below the line**: This tells us if the inequality is ">" or "<".
2. **Determine the line’s slope**:
   - If the line rises steeply, it’s likely **32x**.
   - If it’s less steep, **23x** may be the slope.

Could you share details about the graph's shading and line slope? This will help in selecting the correct inequality.

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Would you like further assistance on determining which inequality matches the graph?

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1. How can we identify the shaded region’s relation to the line?
2. What does a positive or negative slope imply for inequalities?
3. How do different slopes impact the steepness of the line?
4. What are the signs of linear inequalities, and how do they affect shading?
5. How can we interpret y-intercepts in linear inequalities?

**Tip:** Observing the shaded region (above or below) is key to identifying whether the inequality is ">" or "<".

Learn how to determine the correct inequality represented by a graph. This problem involves analyzing slope, y-intercept, and shading in coordinate geometry, suitable for students in Grades 8-10.

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