1. What is the Constant of Proportionality?

The constant of proportionality (k) is the ratio between two directly proportional quantities. It describes how one quantity changes in relation to another.

2. How Does the Calculator Work?

The calculator uses the proportionality equation:

Where:

• \( k \) — Constant of proportionality (dimensionless)
• \( y_2 \) — Second y-value
• \( y_1 \) — First y-value
• \( x_2 \) — Second x-value
• \( x_1 \) — First x-value

Explanation: The equation calculates the rate of change between two variables in a proportional relationship.

3. Importance of Proportionality Constant

Details: The constant of proportionality is fundamental in physics, mathematics, and engineering for describing linear relationships between variables.

4. Using the Calculator

Tips: Enter any two points (x₁,y₁) and (x₂,y₂) from a proportional relationship. Ensure x₂ - x₁ ≠ 0 for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does the constant of proportionality represent?
A: It represents the ratio between two directly proportional quantities (how much y changes per unit change in x).

Q2: What are some real-world examples?
A: Speed (distance/time), density (mass/volume), and unit pricing (cost/quantity) are common examples.

Q3: How is this different from slope?
A: In direct proportionality, the constant is identical to the slope when the relationship passes through the origin (0,0).

Q4: What if the denominator is zero?
A: The calculation is undefined because division by zero is impossible. This indicates a vertical line (not a proportional relationship).

Q5: Can this be used for non-linear relationships?
A: No, this calculator is specifically for linear proportional relationships where y = kx.