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The question asks which equation has a constant of proportionality equal to \( \frac{1}{2} \). The constant of proportionality in a linear equation of the form \( y = mx \) is the coefficient of \( x \), which is \( m \).

Let's analyze the options:

- **A: \( y = 2x \)** — The constant of proportionality here is 2.
- **B: \( y = 4x \)** — The constant of proportionality is 4.
- **C: \( y = \frac{3}{6}x \)** — Simplifying \( \frac{3}{6} \), we get \( y = \frac{1}{2}x \), so the constant of proportionality is \( \frac{1}{2} \).
- **D: \( y = \frac{3}{4}x \)** — The constant of proportionality is \( \frac{3}{4} \).

So, the correct answer is **C**: \( y = \frac{3}{6}x \), as this equation simplifies to \( y = \frac{1}{2}x \), with a constant of proportionality of \( \frac{1}{2} \).

Would you like more details or have any further questions?

Here are five questions to expand on this concept:
1. What does the constant of proportionality represent in a linear equation?
2. How do you simplify fractions in an equation?
3. Can constants of proportionality be negative? If so, what does that imply?
4. How would you graph a line with a constant of proportionality equal to 1/2?
5. How can you determine the constant of proportionality from a table of values?

**Tip:** The constant of proportionality can be seen as the "rate of change" or "slope" in a linear equation, which determines how quickly \( y \) changes with respect to \( x \).

Which equation has a constant of proportionality equal to \( \frac{1}{2} \)?
A: \( y = 2x \)
B: \( y = 4x \)
C: \( y = \frac{3}{6}x \)
D: \( y = \frac{3}{4}x \)

Discover how to identify the constant of proportionality in linear equations. This problem demonstrates key algebraic concepts and is suitable for students in Grade 7-8. Learn how to solve equations like \( y = \frac{3}{6}x \) to find the constant of proportionality.

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