Year 8: Solving proportionality relationships

What is proportionality?

Proportional relationships mean that two quantities change together in a predictable way. When one quantity doubles, the other doubles. When one triples, the other triples, and so on.

Key Concepts:

• Direct Proportion: y = kx (where k is the constant of proportionality) As x increases, y increases at the same rate.
• Inverse Proportion: x = k/y (where k is the constant of proportionality) As y increases, x decreases at the same rate.

How to Solve Direct Proportion Problems:

1. Find the Constant of Proportionality (k): If you have two values for x and y, calculate k = y/x.
2. Use the Formula: Once you know k, use the formula y = kx to find y if you know x, or find x if you know y.

How to Solve Inverse Proportion Problems:

1. Find the Constant of Proportionality (k): Calculate k = x * y.
2. Use the Formula: Use the formula x = k/y or y = k/x.

Example (Direct): If y is directly proportional to x, and x = 4 when y = 8, find y when x = 12.

k = 8/4 = 2. Therefore, y = 2 * 12 = 24.

Example (Inverse): If x is inversely proportional to y, and x = 6 when y = 3, find x when y = 6.

k = 6 * 3 = 18. Therefore, x = 18/6 = 3.