1. What is Direct Variation?

Direct variation describes a simple relationship between two variables where one is a constant multiple of the other. When two quantities vary directly, their ratio remains constant. This is expressed as y = kx, where k is the constant of variation.

2. How Does the Calculator Work?

The calculator uses the direct variation formulas:

Where:

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

Explanation: The calculator can find any one missing value when the other two are known.

3. Understanding the Constant of Variation

Details: The constant (k) represents the ratio between y and x in a direct variation relationship. It remains unchanged as x and y change proportionally.

4. Using the Calculator

Tips:

• To find k: Enter values for x and y
• To find y: Enter values for k and x
• To find x: Enter values for k and y

Note: x and k cannot be zero in their respective calculations.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I know if two variables have direct variation?
A: If the ratio y/x is always the same for all data pairs, they vary directly.

Q3: Can the constant of variation be negative?
A: Yes, a negative constant means y decreases as x increases (or vice versa), maintaining a constant ratio.

Q4: What are real-world examples of direct variation?
A: Distance and time at constant speed (d = rt), cost and number of items at fixed price (C = pn).

Q5: How is direct variation represented graphically?
A: It's represented by a straight line passing through the origin (0,0) with slope equal to k.