Constant of Variation

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities.

The formula for direct variation is

y=kx (or y=kx )

where k is the constant of variation.

Example 1:

If y varies directly as x and y=15 when x=24 , find x when y=25 .

Find the constant of variation.

k= y x = 15 24 = 5 8 y= 5 8 x

To find x , substitute 25 for y .

25= 5 8 x x=40

The constant of variation in an indirect variation is the constant (unchanged) product between two variable quantities.

The formula for indirect variation is

xy=k (or y= k x )

where k is the constant of variation.

Example 2:

If it takes 4 hours at an average speed of 90 km/h to do a certain journey, how long would it take at 120 km/h?

Find the constant of variation.

k = speed · time

k=904=360

Then,

time= k speed = 360 120 =3 hours.