Brainlag PlusSolve proportion problems with the unitary method and with formulae y = kx and y = k/x, recognise proportion in tables and graphs, and (Higher) work with y ∝ x², y ∝ 1/x² and y ∝ √x.
Direct and inverse
Direct proportion: y = kx.
Double x and y doubles; y ÷ x is always k. The graph is a straight line through (0, 0).
Inverse proportion: y = k/x. Double x and y halves; x × y is always k. The graph is a curve that gets closer to both axes.
- y is inversely proportional to x, and y = 6 when x = 4
- k = 4 × 6 = 24, so y = 24/x
- when x = 3, y = 24 ÷ 3 = 8
If 4 builders take 6 days to build a wall, the total work is 4 × 6 = 24 builder-days. So 3 builders take 24 ÷ 3 = 8 days. More builders, fewer days: that is inverse proportion.
The rest of this lesson and its 7 practice questions are in Plus.
Screen 1 of 3, free to read.
- 7 exam-style questions, marked as you go, each with a worked solution
- The Graphing Calculator beside every question
- Anything you get wrong is saved to your flashcards