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MathidiaMathematics Academy
Proportion and rates of change
Lesson 40 of 75
Review

Proportion graphs

Objective. Distinguish direct proportion from other linear relationships.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Proportion graphs distinguish direct proportion, which always produces a straight line through the origin, from other linear relationships that have a non-zero y-intercept. A line represents direct proportion only if it passes exactly through (0, 0), since doubling x must always double y with no constant offset. A graph like y = 2x + 3 looks linear but is not direct proportion because it does not pass through the origin; doubling x does not double y. Testing whether a line passes through the origin is the quickest way to confirm or reject direct proportion from a graph or its equation.

Worked example

Which of these graphs represents a situation of direct proportion between x and y? Choose the correct equation.

Options
  • y = 4x + 2
  • y = 4x
  • y = 4x − 1
  • y = x²
  1. 1Direct proportion requires a straight line through the origin, so c must equal 0.
  2. 2Check y = 4x + 2: this has a y-intercept of 2, so it is not direct proportion.
  3. 3Check y = 4x: this has no constant term, so it passes through the origin.
  4. 4Since y = 4x satisfies y = kx exactly, it represents direct proportion.

Answer: y = 4x

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Common mistake. Pupils often assume any straight-line graph represents direct proportion, overlooking that the line must pass through the origin with no constant term. Always check the graph crosses (0, 0) before confirming direct proportion.

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