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The inequality you've provided is \( y < 3x - 1 \).

This represents a linear inequality, which can be interpreted graphically on a coordinate plane. Here’s a step-by-step explanation to clarify:

### 1. **Equation Interpretation**:
   - The inequality \( y < 3x - 1 \) means that the values of \( y \) are less than the values of the line \( y = 3x - 1 \).
   - The line \( y = 3x - 1 \) is a straight line with:
     - **Slope**: \( 3 \), meaning for every increase of 1 in \( x \), \( y \) increases by 3.
     - **Y-intercept**: \( -1 \), meaning the line crosses the y-axis at \( -1 \).

### 2. **Graphing the Line**:
   - First, graph the line \( y = 3x - 1 \) using the slope and intercept. 
     - Start at \( (0, -1) \) on the y-axis.
     - Use the slope \( 3 \) to find other points (e.g., \( (1, 2) \) and \( (-1, -4) \)).

### 3. **Shading the Region**:
   - Since the inequality is \( y < 3x - 1 \) (not \( \leq \)), you would draw the line as a **dashed line** to indicate that points on the line are *not included* in the solution.
   - You shade the region **below** the line, as \( y \) is less than the expression \( 3x - 1 \).

### 4. **Solution Set**:
   - The solution includes all points in the shaded region, representing all combinations of \( x \) and \( y \) that satisfy \( y < 3x - 1 \).

Would you like to explore more about how this inequality works or see an example? Feel free to ask for any clarifications.

Here are 5 related questions:
1. How do you find the slope and intercept from a linear equation?
2. What does the inequality \( y \leq 3x - 1 \) represent instead of \( y < 3x - 1 \)?
3. How do you know when to draw a solid vs. dashed line in inequalities?
4. How can you test if a point satisfies the inequality \( y < 3x - 1 \)?
5. What changes if the inequality was \( y > 3x - 1 \)?

**Tip**: Always remember that the direction of the inequality (less than or greater than) determines which region of the graph you will shade.

Understand how to graph the linear inequality y < 3x - 1. This problem covers key algebraic concepts including slope, y-intercept, and how to shade the correct region for inequalities. Ideal for students in Grades 8-10.

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