1. What is the Constant of Inverse Variation?

Inverse variation describes a relationship where the product of two variables is constant. When one variable increases, the other decreases proportionally to maintain the same product.

2. How Does the Calculator Work?

The calculator uses the inverse variation formula:

Where:

• \( k \) — Constant of inverse variation
• \( x \) — First variable
• \( y \) — Second variable

Explanation: The constant k remains the same for all pairs of (x,y) that are inversely related. If x doubles, y must halve to maintain the same k.

3. Importance of Inverse Variation

Details: Inverse variation relationships appear in many real-world situations like speed vs. travel time, price vs. demand, and resistance vs. current in electricity.

4. Using the Calculator

Tips: Enter any two variables x and y that are inversely related. The calculator will determine their constant of variation k.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between direct and inverse variation?
A: In direct variation, y = kx (ratio is constant). In inverse variation, xy = k (product is constant).

Q2: Can either x or y be zero?
A: No, in inverse variation neither variable can be zero since their product must be a non-zero constant.

Q3: How is this different from joint variation?
A: Joint variation involves more than two variables (e.g., z = kxy), while inverse variation specifically refers to the two-variable case.

Q4: What are some real-world examples?
A: Boyle's Law (pressure vs. volume of gas), illumination vs. distance from light source, number of workers vs. time to complete a job.

Q5: How do I graph an inverse variation?
A: The graph is a hyperbola with the equation y = k/x. It never touches the x or y axes.