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Ratio & ProportionStudy Notes

Worked Example 1: Basic Direct Proportion

Part of Proportion Graphs — GCSE Mathematics

This study notes covers Worked Example 1: Basic Direct Proportion within Proportion Graphs for GCSE Mathematics. Revise Proportion Graphs in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 4 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 5

Practice

14 questions

Recall

4 flashcards

Worked Example 1: Basic Direct Proportion

y is directly proportional to x. When x = 5, y = 20. Find y when x = 8.

Step 1 Set up the equation

y ∝ x means y = kx

Step 2 Find k using given values

20 = k × 5

k = 20 ÷ 5 = 4

Step 3 Find y when x = 8

y = 4 × 8 = 32

Keep building this topic

Read this section alongside the surrounding pages in Proportion Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Method: Finding the ConstantWorked Example 2 (Higher): Proportional to SquareWhat Is Direct Proportion?Key Facts

Practice Questions for Proportion Graphs

Which of the following describes the graph of a direct proportion relationship?

  • A. A curved line passing through the origin
  • B. A straight line passing through the origin
  • C. A straight line that crosses the y-axis above zero
  • D. A U-shaped curve symmetric about the y-axis
1 markfoundation

Aisha says: 'Because the graph of y against x is a straight line, y must be directly proportional to x.' Is Aisha correct? Explain your answer.

2 marksstandard

Quick Recall Flashcards

Direct vs Inverse
Direct: both increase together (y ∝ x). Inverse: one increases, other decreases (y ∝ 1/x).
Finding k
Use given values to find constant k, then apply to new values

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Method: Finding the Constant

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Worked Example 2 (Higher): Proportional to Square