1. What is Constant Variation?

Constant variation describes a relationship where the ratio between two variables remains unchanged. In the equation \( k = \frac{y}{x} \), \( k \) is the constant of variation that relates variables \( y \) and \( x \).

2. How Does the Calculator Work?

The calculator uses the constant variation formula:

Where:

• \( k \) — Constant of variation
• \( y \) — Dependent variable value
• \( x \) — Independent variable value

Explanation: The constant \( k \) remains the same for all corresponding values of \( x \) and \( y \) in a directly proportional relationship.

3. Applications of Constant Variation

Details: Constant variation is used in physics (Hooke's Law), economics (price elasticity), chemistry (Boyle's Law), and many other fields where proportional relationships exist.

4. Using the Calculator

Tips: Enter known values for \( y \) and \( x \) (x cannot be zero). The calculator will compute the constant of variation \( k \).

5. Frequently Asked Questions (FAQ)

Q1: What does a constant variation represent?
A: It represents the fixed ratio between two variables that change proportionally.

Q2: What's the difference between constant variation and slope?
A: In linear relationships, the constant of variation is equivalent to the slope of the line \( y = kx \).

Q3: Can the constant of variation be negative?
A: Yes, when one variable increases while the other decreases (inverse variation).

Q4: How is this different from inverse variation?
A: Direct variation uses \( y = kx \), while inverse variation uses \( y = k/x \).

Q5: What are real-world examples of constant variation?
A: Speed (distance/time), density (mass/volume), and conversion factors between measurement units.