Alexander graphed a linear inequality on the coordinate plane.

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

B.y > 32x −3

C.y > 23x −3

D.y < 23x −3


To identify which inequality is represented by Alexander's graph, here’s what we should consider:

1. **Slope of the Line**: In each option, the slope (m) and y-intercept (b) vary. We need to find the correct combination of these values.

2. **Inequality Sign**: The inequality symbol (`<` or `>`) affects whether the shading is above or below the line. If `y >` or `y ≥`, the shading will be above the line; if `y <` or `y ≤`, the shading will be below the line.

3. **Testing the Options**:
   - Options **A** and **B** have a slope of \( \frac{3}{2} \) and a y-intercept of -3.
   - Options **C** and **D** have a slope of \( \frac{2}{3} \) and a y-intercept of -3.

Without the graph, a more specific answer can’t be confirmed, but if you can provide any details on the shading and direction of the line, I can determine the exact inequality.

Would you like further clarification or assistance on how these inequalities would look on a graph?

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### Further Questions
1. What does the graph reveal about the position of the shaded area relative to the line?
2. Can you identify the slope and y-intercept on the graph to assist in narrowing down the options?
3. Do you observe a dashed or solid line in the graph?
4. Is the shaded area above or below the line in the graph?
5. How would you graph a similar inequality from scratch?

**Tip:** Remember that the inequality direction (`<` or `>`) directly impacts the shading placement on the graph.

Alexander graphed a linear inequality on the coordinate plane. Which inequality is best represented by the graph?
A. y < 3/2x − 3
B. y > 3/2x − 3
C. y > 2/3x − 3
D. y < 2/3x − 3

Learn how to identify a linear inequality based on its graph with a focus on slope, y-intercept, and shading direction. This problem explores key algebraic concepts like graphing linear inequalities and interpreting shading to determine inequality symbols. Ideal for students in Grades 8-10.

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