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.
