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: $y=6\times 3=18$. 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.