1. What is Direct Variation?

Direct variation describes a simple relationship between two variables where one is a constant multiple of the other. When one variable changes, the other changes in proportion to the first.

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 varies directly with x, with k being the constant ratio between them.

3. Applications of Direct Variation

Details: Direct variation appears in many real-world situations like Hooke's Law (spring force), Ohm's Law (electrical current), and speed-distance-time relationships.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: How is direct variation different from inverse variation?
A: In direct variation, y increases as x increases. In inverse variation, y decreases as x increases (y = k/x).

Q2: What does the constant of variation represent?
A: The constant k represents the ratio between y and x (k = y/x) and remains unchanged for all values.

Q3: Can direct variation have a negative constant?
A: Yes, a negative constant means y decreases as x increases, maintaining a constant negative ratio.

Q4: 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.

Q5: What are some real-world examples?
A: Examples include wages (directly proportional to hours worked), distance (directly proportional to time at constant speed), and cost (directly proportional to quantity).