https://file.aiquickdraw.com/mathbot/file/1729868603448d7nh1ggj.jpg

The given graph shows a shaded region above a dashed line, which suggests that the inequality is "greater than" or "greater than or equal to," but since the line is dashed, the inequality will be strict ("greater than").

Let's break it down:

1. **Slope of the line**: The line crosses the y-axis at \( -3 \) and has a slope of \( \frac{3}{2} \), since for every 2 units moved horizontally, the line moves up 3 units vertically.
   
2. **Equation of the boundary line**: The equation of the line is \( y = \frac{3}{2}x - 3 \).

3. **Inequality direction**: The shaded region is **above** the line, indicating that the inequality should be \( y > \frac{3}{2}x - 3 \).

Thus, the inequality best represented by the graph is **option A: \( y > \frac{3}{2}x - 3 \)**.

Would you like more details or have any questions about this? Here are five related questions you might find helpful:

1. How do you determine the slope of a line from a graph?
2. What does a dashed line represent in inequalities compared to a solid line?
3. How do you know which side of the line to shade in an inequality graph?
4. What are the steps to convert an equation of a line into an inequality?
5. How can you graph an inequality with two variables?

**Tip**: The inequality sign (greater than or less than) is determined by whether the region is above or below the line.

Which inequality is best represented by the graph?

Learn how to solve and graph linear inequalities like y > 3/2x - 3, focusing on identifying the slope and shading the correct region of the graph. This problem is ideal for students in Grade 8 and Algebra 1.

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