1. What is Direct Variation?

Direct variation describes a simple relationship between two variables where one is a constant multiple of the other. It follows the equation y = kx, where k is the constant of variation.

2. How Does the Calculator Work?

The calculator uses the direct variation equation:

Where:

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

Explanation: The equation shows that y changes directly as x changes. The constant k remains the same throughout the relationship.

3. Importance of Direct Variation

Details: Direct variation is fundamental in mathematics and physics, describing proportional relationships in phenomena like Hooke's Law, Ohm's Law, and many other physical laws.

4. Using the Calculator

Tips: Enter the constant of variation (k) and a value for the independent variable (x). The calculator will compute the corresponding y value.

5. Frequently Asked Questions (FAQ)

Q1: What does the constant of variation represent?
A: The constant k represents the ratio of y to x in the relationship. It determines how rapidly y changes with respect to x.

Q2: How is direct variation different from linear relationships?
A: All direct variations are linear, but not all linear relationships are direct variations. Direct variation must pass through the origin (0,0).

Q3: What are real-world examples of direct variation?
A: Examples include distance and time at constant speed, cost and number of items at fixed price, and force and acceleration (F=ma).

Q4: Can the constant of variation be negative?
A: Yes, a negative k indicates an inverse relationship where y decreases as x increases.

Q5: How do I find the constant of variation from data points?
A: Calculate k = y/x for any (x,y) pair in the relationship (except when x=0).