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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 = k x (or y = k x )

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

x y = 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 = 90 4 = 360

Then,

time = k speed = 360 120 = 3  hours .

 

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