Direct & inverse proportion graphs
AQA GCSE Maths revision on Direct & inverse proportion graphs. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 17 practice questions on this topic.
Sample questions (3 of 17)
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Question 1
Which shape describes the graph of y = k/x for x > 0?
- A) Straight line through the origin
- B) Parabola
- C) Hyperbola
- D) Circle
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Answer: Hyperbola
When two variables are inversely proportional, as one increases, the other decreases at a non-linear rate. This relationship, defined by y = k/x, produces a characteristic curve called a hyperbola that approaches the axes but never touches them.
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Question 2
A student claims that for y = kx, doubling x will result in y remaining the same. Why is this incorrect?
- A) Because y is inversely proportional to x
- B) Because the relationship is direct
- C) Because y is independent of x
- D) Because the graph should be a curve
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Answer: Because the relationship is direct
In a direct proportion equation, y = kx, the variable y is linearly dependent on x. If you multiply the input x by any constant factor, the output y must be multiplied by that same factor for the ratio y/x to remain constant.
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Question 3
If a graph of y against x is a straight line passing through the origin (0,0), what is the relationship between x and y?
- A) Inverse proportion
- B) Direct proportion
- C) Quadratic relationship
- D) Exponential growth
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Answer: Direct proportion
For two variables to be directly proportional, the graph must be a straight line that passes through the origin. This represents the equation y = kx, where k is the gradient of the line.
Want to test yourself on the remaining cards for this topic?
14 more questions on Direct & inverse proportion graphs — plus mistakes tracking and spaced repetition across the whole Maths spec.