1. What is Inverse Variation?

Inverse variation describes a relationship between two variables where their product is constant. When one variable increases, the other decreases proportionally, and vice versa.

2. How Does the Calculator Work?

The calculator uses the inverse variation formula:

Where:

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

Explanation: The formula shows that y is inversely proportional to x, with k being the constant that relates the two variables.

3. Applications of Inverse Variation

Details: Inverse variation appears in physics (Boyle's Law), engineering, economics, and many real-world situations where one quantity decreases as another increases.

4. Using the Calculator

Tips: Enter the constant of variation (k) and a value for x (x cannot be zero). The calculator will compute the corresponding y value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between direct and inverse variation?
A: In direct variation, y = kx (both increase together). In inverse variation, y = k/x (one increases as the other decreases).

Q2: Can x be zero in inverse variation?
A: No, x cannot be zero because division by zero is undefined.

Q3: How do I find the constant of variation k?
A: If you know one pair of (x,y) values, k = x × y.

Q4: What does the graph of inverse variation look like?
A: It's a hyperbola that never touches the x or y axes.

Q5: Are there real-world examples of inverse variation?
A: Yes! Examples include: speed vs. travel time for a fixed distance, number of workers vs. time to complete a job, and pressure vs. volume in gases (Boyle's Law).