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 r2

Change into a formula:

y = kr2

Sub. to work out k:

80 = k x 42

k = 5

So:

y = 5r2

And:

2.45 = 5r2

Working out r:

r = 0.7

Possible direct variation questions:

x p

t h2

s 3v

c i

g u3 g = ku3

c = ki

s = k3vt = kh2

x = kp

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 = 30So

: y = 30/r

And:

7.5 = 30/r

Working out r:

r = 16 (not 2)

Possible inverse variation questions:

x 1/p

t 1/h2

s 1/3v

c 1/i

g 1/u3 g = k/u3

c = k/i

s = k/3v

t = k/h2

x = k/p