Year 9: Solving proportionality relationships

What is Proportionality?

Proportionality means that two quantities are related in a specific way. When one quantity changes, the other changes in a predictable, consistent manner. This is often represented by the equation 𝑦 = 𝑘𝑥, where 𝑦 and 𝑥 are variables and 𝑘 is a constant called the constant of proportionality.

Key Concepts

• Constant of Proportionality (k): This constant tells you how much one quantity changes for every unit change in the other.
• Direct Proportionality: As one quantity increases, the other also increases.
• Inverse Proportionality: As one quantity increases, the other decreases.

Solving Proportionality Problems

Direct Proportionality

Example: If y = 6x, find y when x = 3.

Substitute x = 3 into the equation: y = 6 * 3 = 18. Therefore, y = 18.

Inverse Proportionality

Example: If y = 10/x, find y when x = 5.

Substitute x = 5 into the equation: y = 10 / 5 = 2. Therefore, y = 2.

Remember!

• Always identify if it's direct or inverse proportionality.
• Make sure your units are consistent.