Inverse proportion

Objective. Recognise and solve introductory inverse proportion problems.

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2. Worked example
3. Practice
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Learn: the key idea

Inverse proportion means one quantity increases as the other decreases, such that their product stays constant, described by the equation y = k/x. To find k, multiply a known pair of x and y values together, then use that constant to find any other matching pair. For example, if y is inversely proportional to x and y = 8 when x = 3, then k = 8 × 3 = 24, giving the equation y = 24/x, so when x = 6, y = 24 ÷ 6 = 4. Graphically, inverse proportion produces a curve that never touches either axis, unlike the straight line of direct proportion.

Worked example

y is inversely proportional to x. When x = 4, y = 15. Find the value of y when x = 5.

1 $Use y = k/x and substitute the known values: 15 = k/4.$
2 $Multiply both sides by 4 to find k: k = 60.$
3 $Write the equation: y = 60/x.$
4 $Substitute x = 5: y = 60 \div 5 = 12.$

Answer: y = 12

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Common mistake. Pupils sometimes use the direct proportion method of dividing y by x to find k in an inverse proportion problem, instead of multiplying them together. In inverse proportion, multiply the paired values to find k, not divide.

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