0580

Proportion

Algebra and Sequences

Recognising it

  • In direct proportion the two quantities rise and fall together, and their ratio never changes
  • Written in symbols, y ∝ x, which becomes y = kx
  • Doubling one quantity doubles the other, and halving one halves the other
  • Plotted on axes the relationship is a straight line through the origin, and k is its steepness
A graph of a directly proportional relationship on axes running from −5 to 5: a single straight line passing exactly through the origin, so doubling x doubles y
Source: Direct proportion by Save My Exams
  • The wording in question papers is usually just "w is proportional to x": the word "directly" is often left out altogether
Worked example

Finding the equation and using it

p is proportional to q. When q = 9, p = 45. Find p when q = 14.

Solution:

  • The statement gives the equation p = kq
  • Substitute the given pair: 45 = k × 9
  • Divide by 9: k = 5
  • The finished equation is p = 5q
  • Substitute q = 14: p = 5 × 14
  • So p = 70