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Directly Proportional

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Key Stage 4


When two variables are directly proportional when one variable is multiplied by a factor, the other variable is multiplied by the same factor.

About Direct Proportionality

A scatter graph showing a directly proportional relationship has line with a linear gradient that passes through zero (it has a y-intercept of zero).
On a proportional scatter graph when one variable doubles, the other doubles or when one triples the other triples.
When two variables are directly proportional when any value for y is divided by its corresponding value for x it will always give a constant value.
Two variables are said to be directly proportional when they always vary by the same ratio.

Exam Marks

Straight line [1 mark]
Passing through zero / passing through the origin [1 mark]


This scatter graph shows a linear relationship that is directly proportional where x doubles, y doubles.

\(y = mx\)

Where m, the gradient, is positive.



Directly proportional, pages 158-159, 282, GCSE Physics; Third Edition, Oxford University Press, AQA


Direct proportional, page 427, GCSE Combined Science, Pearson Edexcel