1. What is the Constant of Proportionality?

The constant of proportionality (k) is the constant ratio between two directly proportional quantities (y and x) in the relationship y = kx. It describes how much y changes for a unit change in x.

2. How Does the Calculator Work?

The calculator uses the proportionality formula:

Where:

• \( k \) — Constant of proportionality (dimensionless)
• \( y \) — Dependent variable (fraction)
• \( x \) — Independent variable (fraction)

Explanation: The calculator accepts fractions as input, computes the ratio, and simplifies the resulting fraction when possible.

3. Importance of Proportionality Constant

Details: The constant of proportionality is fundamental in mathematics and physics, describing linear relationships in equations, graphs, and real-world scenarios like scaling recipes or converting units.

4. Using the Calculator

Tips: Enter y and x as fractions (e.g., 3/4) or whole numbers. The calculator will return k as a simplified fraction or decimal. X cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if my inputs are decimals instead of fractions?
A: The calculator will accept decimal inputs and return a decimal result.

Q2: Can k be negative?
A: Yes, if y and x have opposite signs, k will be negative, indicating an inverse relationship.

Q3: What does it mean if k = 1?
A: When k = 1, y and x are equal (y = x). This represents direct 1:1 proportionality.

Q4: How is this different from slope?
A: In y = kx, k is both the constant of proportionality and the slope of the line. The concepts are identical in this context.

Q5: Can I use mixed numbers (like 1 1/2)?
A: Convert mixed numbers to improper fractions first (1 1/2 becomes 3/2) for accurate results.