2. Direct proportion If one variable is in direct proportion to another (sometimes called direct variation) their relationship is described by: p  t p = kt Where the “Alpha” can be replaced by an “Equals” and a constant “k” to give : e.g. y is directly proportional to the square of r. If r is 4 when y is 80, find the value of r when y is 2.45. Write out the variation: y  r 2 Change into a formula: y = kr 2 Sub. to work out k: 80 = k x 4 2 k = 5 So: y = 5r 2 And: 2.45 = 5r 2 Working out r: r = 0.7 Possible direct variation questions: x  p t  h 2 s  3  v c   i g  u 3 g = ku 3 c = k  i s = k 3  v t = kh 2 x = kp

3. Inverse proportion If one variable is inversely proportion to another (sometimes called inverse variation) their relationship is described by: p  1/t p = k/t Again “Alpha” can be replaced by a constant “k” to give : e.g. y is inversely proportional to the square root of r. If r is 9 when y is 10, find the value of r when y is 7.5. Write out the variation: y  1/  r Change into a formula: y = k/  r Sub. to work out k: 10 = k/  9 k = 30 So: y = 30/  r And: 7.5 = 30/  r Working out r: r = 16 (not 2) Possible inverse variation questions: x  1/p t  1/h 2 s  1/ 3  v c  1/  i g  1/u 3 g = k/u 3 c = k/  i s = k/ 3  v t = k/h 2 x = k/p