Direct and Inverse Proportion (Algebraic)

This lesson covers the algebraic treatment of direct and inverse proportion, primarily aimed at Higher tier students in the Edexcel GCSE Mathematics (1MA1) specification. You will learn to set up proportionality equations, find constants, and use them to solve problems. Graphical representations of proportional relationships are also covered.

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Key Vocabulary

Symbol/Term	Meaning
y is proportional to x	y = kx (written y ∝ x)
k	The constant of proportionality
∝	The proportionality symbol (means "is proportional to")
Direct proportion	As one variable increases, the other increases at the same rate
Inverse proportion	As one variable increases, the other decreases

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Direct Proportion

If y is directly proportional to x, we write:

y ∝ x, which means y = kx

To find k, substitute a known pair of values.

y ∝ x (y is directly proportional to x)

Worked Example 1: y is directly proportional to x. When x = 4, y = 20. Find the equation and the value of y when x = 7.