9.1 Class notes. Direct, inverse, joint and combined
variation
Direct Variation, y = kx where k is always the same number.
Example 1.
The value of y varies directly with x, and y = 20 when
x = 2. Find y when x = 8.
Inverse or Indirect Variation, where when one of the variables increases, the
other one decreases
where k is always the same number.
Example 2.
The value of y varies inversely with x, and y = 4 when
x = 3. Find x when y = 6.
Example 3.
For the Choir fundraiser, the number of tickets Allie can buy is inversely
proportional to the price of the tickets. She can afford 15 tickets that cost $5
each. How many tickets can Allie buy if each cost $3?
Joint Variation, where more than two variables are related directly z=kxy
Example 4
Supposed x varies jointly with y and the square root of z. When x = –18 and y =
2, then z = 9. Find y when x = 10 and z = 4.
Combined Variation, which involves a combination of direct or joint
variation, and indirect variation
Example 5
y varies jointly as x and w and inversely as the square of z. Find the equation
of variation when y = 100, x = 2, w = 4, and z = 20.