Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.

Since I don’t have access to the specific options for your question, I'll provide a general analysis of the linear inequality \( y > \frac{3}{4}x - 2 \), and you can match it with the options given.

Here are key facts that can help you identify which statements are true:

### 1. **Slope of the boundary line**:
The slope of the line \( y = \frac{3}{4}x - 2 \) is positive because the coefficient of \(x\) is \( \frac{3}{4} \), a positive fraction. The slope describes the line's steepness and direction (rising from left to right).

### 2. **Y-intercept**:
The y-intercept of the line \( y = \frac{3}{4}x - 2 \) is \( -2 \). This means the line crosses the y-axis at the point \( (0, -2) \).

### 3. **Dashed Line**:
Because the inequality is \( y > \frac{3}{4}x - 2 \), the line \( y = \frac{3}{4}x - 2 \) is not included in the solution. Therefore, the boundary line is **dashed** (as opposed to solid). A solid line is used if the inequality includes "or equal to" (e.g., \( \geq \)).

### 4. **Shaded region**:
The inequality \( y > \frac{3}{4}x - 2 \) represents the area **above** the boundary line. This includes all points where the \(y\)-value is greater than the corresponding value on the line.

### 5. **Points on the line are not solutions**:
Since the inequality is strict (\(>\)), any points that lie directly on the line \( y = \frac{3}{4}x - 2 \) are **not** part of the solution.

### Summary of likely true statements:
- The slope of the boundary line is **positive**.
- The y-intercept of the boundary line is **-2**.
- The graph represents a region **above** a dashed boundary line.

These points should match three of your options. Compare these insights to the options available to select the correct ones.

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Would you like more details or explanations on any part?  
Here are five related questions for further practice:

1. What happens to the solution if the inequality changes to \( y \geq \frac{3}{4}x - 2 \)?
2. How would the graph change if the slope was negative, e.g., \( y > -\frac{3}{4}x - 2 \)?
3. How do you test whether a point is a solution to a linear inequality?
4. What effect does changing the y-intercept have on the graph of the inequality?
5. Can a point below the line ever be a solution for \( y > \frac{3}{4}x - 2 \)?

**Tip**: Always remember to shade **above** the line for \(y >\) inequalities, and below the line for \(y <\) inequalities.

Explore the key concepts behind the linear inequality y > 3/4x - 2, including slope, y-intercept, and how to graph the inequality. Learn how to determine the region of solutions for students in Grades 8-10.

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