Algebra Period 3 (Monday)

Direct Variation, Indirect Variation and Joint Variation: 12-5 TO 12-7


DIRECT VARIATION
As x increases, y also increases (graphs as a LINE)
or as x decreases, y also decreases
x and y go in the SAME DIRECTION
For example: y = 2x
the "2" is called the constant of variation and is "k" in the formula:
y = kx
To find k, you need one (x, y) coordinate to solve.
It's like solving for "m" in y = mx + b, but there is no b!
Example: y varies directly with x. When y = 8, x = 2. Find y when x = 3.
FORMULA FOR DIRECT VARIATION: y = kx
PLUG IN THE (x, y):
8 = k(2)
SOLVE FOR k:
k = 4
WRITE THE EQUATION:
y = 4x
PLUG IN VARIABLE GIVEN:
y = 4(3)
SOLVE FOR MISSING VARIABLE:
y = 12

INDIRECT VARIATION
As x increases, y decreases (graphs as a RATIONAL function...I'll show you it in class)
x and y go in OPPOSITE DIRECTIONS
For example: y = 2/x
the "2" is still called the constant of variation and is "k" in the formula:
y = k/x
To find k, you need one (x, y) coordinate to solve.
Example: y varies indirectly with x. When y = 8, x = 2. Find y when x = 3.
FORMULA FOR INDIRECT VARIATION:
y = k/x
PLUG IN THE (x, y):
8 = k/2
SOLVE FOR k:
k = 16
WRITE THE EQUATION:
y = 16/x
PLUG IN VARIABLE GIVEN:
y = 16/3
SOLVE FOR MISSING VARIABLE:
y = 5 1/3

JOINT VARIATION
TWO VARIABLES VARY WITH y AT THE SAME TIME!
As x AND z increase, y also increases (graphs as a LINEAR function)
The PRODUCT xz and y go in the SAME DIRECTION
For example: y = 2xz
the "2" is still called the constant of variation and is "k" in the formula:
y = kxz
To find k, you need one (x, y, z) coordinate to solve.
Example: y varies jointly with x and z. When y = 12, x = 2, and z = 3. Find y when x = 3 and z = 5
FORMULA FOR JOINT VARIATION:
y = kxz
PLUG IN THE (x, y, z):
12 = k(2)(3)
SOLVE FOR k:
k = 2
WRITE THE EQUATION:
y = 2xz
PLUG IN VARIABLE GIVEN:
y = 2(3)(5)
SOLVE FOR MISSING VARIABLE:
y = 30