What is important to know about Direct proportion?

If y is directly proportional to x: y = kx, where k is the constant of proportionality.

What is important to know about Direct proportion?

The graph of direct proportion is a straight line through the origin.

What is important to know about Direct proportion?

You can use the unitary method: find the value for 1, then multiply.

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Ratio & Proportion · Foundation & Higher

Direct proportion

Two quantities are in direct proportion if they increase and decrease at the same rate. When one doubles, the other doubles.

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Key facts to remember

1If y is directly proportional to x: y = kx, where k is the constant of proportionality.
2The graph of direct proportion is a straight line through the origin.
3You can use the unitary method: find the value for 1, then multiply.
4If y ∝ x², then y = kx² (direct proportion to the square).

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Formulas

Direct proportion

y = kx

k is constant

Find k

k = y/x (use a known pair)

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Worked examples

Example 1

y is directly proportional to x. When x = 4, y = 20. Find y when x = 7.

Working

y = kx → 20 = k × 4 → k = 5
y = 5x
When x = 7: y = 5 × 7 = 35

Answery = 35

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Common mistakes

✗Not finding k first — always establish the formula before finding new values.

✗Confusing direct proportion (y = kx) with inverse proportion (y = k/x).

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Exam tips

✓Look for the words "proportional to" — they tell you the relationship type.

✓Find k using the given values, then use the formula for the unknown.

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