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 \( y = \frac{k}{x} \) or \( k = x \times y \), where k is the constant of variation.

2. How Does the Calculator Work?

The calculator uses the inverse variation formulas:

Where:

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

Explanation: The calculator can either find the constant of variation (k) when given x and y values, or find the y value when given k and x.

3. Importance of Inverse Variation

Details: Inverse variation is fundamental in physics (e.g., Boyle's Law), engineering, economics, and other sciences where two quantities are inversely proportional.

4. Using the Calculator

Tips:

1. Select whether you want to find the constant (k) or the y value
2. Enter the known values
3. Click Calculate to get the result
4. All values must be positive numbers

5. Frequently Asked Questions (FAQ)

Q1: What are real-world examples of inverse variation?
A: Examples include the relationship between pressure and volume of a gas (Boyle's Law), or between time and speed for a fixed distance.

Q2: How is inverse variation different from direct variation?
A: In direct variation, y = kx (both increase together). In inverse variation, y = k/x (one increases as the other decreases).

Q3: Can the variables in inverse variation be zero?
A: No, neither x nor y can be zero because division by zero is undefined and the product would always be zero.

Q4: How do I graph an inverse variation relationship?
A: The graph is a hyperbola that never touches the x or y axes.

Q5: Can inverse variation have more than two variables?
A: Yes, joint variation can involve multiple variables inversely related (e.g., \( z = \frac{k}{xy} \)).