1. What is Direct Variation?

Direct variation describes a simple relationship between two variables where one is a constant multiple of the other. In mathematical terms, we say that y varies directly with x if y = kx for some constant k (k ≠ 0).

2. How Does the Calculator Work?

The calculator uses the direct variation equation:

Where:

• \( y \) — Dependent variable
• \( x \) — Independent variable
• \( k \) — Constant of variation (k ≠ 0)

Explanation: The equation shows that y changes proportionally with x. The constant k determines the rate of change.

3. Applications of Direct Variation

Details: Direct variation appears in many real-world scenarios including physics (Hooke's Law), economics (direct proportionality), and everyday situations like cost per unit.

4. Using the Calculator

Tips: Enter the constant of variation (k) and the value of x. The calculator will compute the corresponding y value according to the direct variation relationship.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between direct variation and linear equations?
A: All direct variations are linear equations (y = mx + b), but specifically those where b = 0 and m = k.

Q2: How do I find the constant of variation from data points?
A: If you have an (x,y) pair, you can calculate k = y/x (for x ≠ 0).

Q3: Can k be negative in direct variation?
A: Yes, k can be any real number except zero. A negative k indicates an inverse relationship.

Q4: What does the graph of direct variation look like?
A: It's a straight line passing through the origin (0,0) with slope k.

Q5: How is direct variation different from inverse variation?
A: In direct variation, y increases as x increases. In inverse variation (y = k/x), y decreases as x increases.