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. The general form is y = k/x, where k is the constant of variation.

2. How Does the Calculator Work?

The calculator uses the inverse variation equation:

Where:

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

Explanation: Given any (x,y) pair from an inverse variation relationship, the calculator determines the constant k and generates the specific equation.

3. Importance of Inverse Variation

Details: Inverse variation models many real-world phenomena like the relationship between speed and travel time for a fixed distance, or the relationship between resistance and current in electricity (Ohm's Law).

4. Using the Calculator

Tips: Enter any known (x,y) pair from an inverse variation relationship. The calculator will determine the constant k and generate the specific equation. Note that x cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: How is inverse variation different from direct variation?
A: In direct variation (y = kx), y increases as x increases. In inverse variation, y decreases as x increases.

Q2: What are some examples of inverse variation?
A: Examples include: speed vs. travel time (for fixed distance), number of workers vs. time to complete a job, and pressure vs. volume in gases (Boyle's Law).

Q3: Can x be zero in inverse variation?
A: No, x cannot be zero because division by zero is undefined. The function y = k/x has a vertical asymptote at x = 0.

Q4: How do you graph inverse variation?
A: The graph is a hyperbola with two branches in quadrants I and III (if k > 0) or II and IV (if k < 0).

Q5: How do you solve problems with inverse variation?
A: First find the constant k using known values, then use the equation to find unknown values. Remember the product x × y remains constant.