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We are asked to find which of the given linear equations has both a **negative y-intercept** and a **positive slope**.

Linear equations are of the form \( y = mx + b \), where:

- \( m \) represents the slope (how steep the line is).
- \( b \) represents the y-intercept (the value of \( y \) when \( x = 0 \)).

### Let's analyze each option:

1. **\( y = 4x - 3 \):**
   - Slope (\( m \)) = 4 (positive).
   - Y-intercept (\( b \)) = -3 (negative).
   - This equation has a positive slope and a negative y-intercept.

2. **\( y = 3x + 4 \):**
   - Slope (\( m \)) = 3 (positive).
   - Y-intercept (\( b \)) = 4 (positive).
   - This equation has a positive slope but a positive y-intercept.

3. **\( y = -2x + 3 \):**
   - Slope (\( m \)) = -2 (negative).
   - Y-intercept (\( b \)) = 3 (positive).
   - This equation has a negative slope and a positive y-intercept.

4. **\( y = -2x - 5 \):**
   - Slope (\( m \)) = -2 (negative).
   - Y-intercept (\( b \)) = -5 (negative).
   - This equation has a negative slope and a negative y-intercept.

### Conclusion:
The correct equation that has a **negative y-intercept** and a **positive slope** is:
- **\( y = 4x - 3 \)**

Would you like further details or have any questions?

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Here are five questions to explore further:
1. What does the slope represent in a linear equation graph?
2. How does the y-intercept affect the position of the line?
3. Can a line have a zero slope and still intersect the y-axis?
4. How do positive and negative slopes affect the direction of a line?
5. What happens to the graph when both slope and y-intercept are negative?

**Tip:** The slope determines the steepness and direction of the line, while the y-intercept shows where the line crosses the y-axis.

Which of the following equations has a negative y-intercept and a positive slope?

Understand how to identify a linear equation with a negative y-intercept and a positive slope. This problem uses the slope-intercept form of a linear equation (y = mx + b) to help students learn how slopes and y-intercepts affect the position of the line. Suitable for students in Grades 7-9.

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