1. What is the Inverse Variation Equation?

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

2. How Does the Calculator Work?

The calculator uses the inverse variation equation:

Where:

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

Explanation: The equation shows that y is inversely proportional to x. The product of x and y always equals the constant k.

3. Applications of Inverse Variation

Details: Inverse variation appears in physics (Boyle's Law), economics (supply and demand), and engineering (resistance and current).

4. Using the Calculator

Tips: Select which variable you know (k, x, or y), then enter the two known values. The calculator will solve for the unknown.

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 or y be zero in inverse variation?
A: No, neither x nor y can be zero as division by zero is undefined and the product would not remain constant.

Q3: How do I find the constant of variation from a graph?
A: The constant k equals the product of any (x,y) point on the curve (k = x × y).

Q4: What does the graph of inverse variation look like?
A: It's a hyperbola with two branches in the first and third quadrants (if k is positive).

Q5: Can inverse variation have exponents?
A: Yes, generalized forms like y = k/xⁿ are possible, but this calculator uses the basic form (n=1).