How can you tell which function has the greatest 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 kk 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 / 8y=5/8x

To find x, substitute 25 for y.

25=5/8x

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=90⋅4=360

Then,

time = k/speed = 360/120 = 3 hours.