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The problem is asking which equation has a **positive slope** and a **negative y-intercept**. Let's analyze each equation one by one. The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. \( y = 10 - 4x \) 
   - Rewrite it as \( y = -4x + 10 \).
   - Slope: \( m = -4 \) (negative).
   - Y-intercept: \( b = 10 \) (positive).
   - This does not have a positive slope or negative y-intercept.

2. \( y = -4x + 2 \)
   - Slope: \( m = -4 \) (negative).
   - Y-intercept: \( b = 2 \) (positive).
   - This does not meet the requirements.

3. \( y = \frac{3}{4}x + 10 \)
   - Slope: \( m = \frac{3}{4} \) (positive).
   - Y-intercept: \( b = 10 \) (positive).
   - The slope is positive, but the y-intercept is positive, not negative.

4. \( y = -2 + 4x \)
   - Rewrite it as \( y = 4x - 2 \).
   - Slope: \( m = 4 \) (positive).
   - Y-intercept: \( b = -2 \) (negative).
   - This equation has a positive slope and a negative y-intercept, which satisfies the conditions.

**Correct answer: \( y = -2 + 4x \) (or equivalently \( y = 4x - 2 \))**

Would you like any further explanation or details?

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Here are 5 related questions to further your understanding:
1. How do you identify the slope and y-intercept in a linear equation?
2. What happens if both the slope and y-intercept are negative?
3. Can two different equations have the same slope but different y-intercepts? How would their graphs look?
4. How does the slope of a line affect its direction on a graph?
5. How can you graph a line given just its slope and y-intercept?

**Tip:** The slope indicates the steepness of a line, while the y-intercept tells you where the line crosses the y-axis.

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

Learn how to identify a linear equation with a positive slope and a negative y-intercept. This problem involves analyzing different equations to determine which one meets the criteria. Suitable for students in Grades 8-10.

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