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To determine which of the equations represents an inverse variation, let's first recall the definition of inverse variation:

### Inverse Variation:
An inverse variation occurs when two variables are related such that their product is constant. The equation for an inverse variation can be written as:
\[ y = \frac{k}{x}, \]
where \( k \) is a constant.

Now, let's analyze each option:

- **a. \( y = 3x + 2 \)**: This is a linear equation and does not represent an inverse variation.
- **b. \( y = 4x \)**: This is also a linear equation, not an inverse variation.
- **c. \( y = \frac{-4}{x} \)**: This equation fits the form \( y = \frac{k}{x} \), where \( k = -4 \). This represents an inverse variation.
- **d. \( y = -3x + 1 \)**: This is another linear equation and not an inverse variation.

### Answer:
The equation that represents an inverse variation is **c. \( y = \frac{-4}{x} \)**.

Would you like more details on how inverse variation works or any other questions? 

Here are 5 related questions you might consider:
1. How do you identify a direct variation?
2. Can a quadratic equation represent an inverse variation?
3. What is the constant of variation in inverse variation equations?
4. How would you graph an inverse variation?
5. What happens to \( y \) as \( x \) approaches 0 in an inverse variation?

**Tip:** In inverse variation, as one variable increases, the other decreases, keeping their product constant.

Understand inverse variation equations with clear examples. Learn to identify inverse variation using key mathematical concepts and formulas. Suitable for high school students studying algebra and functions.

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