Algebra 2 9.1 Direct, Inverse, & Joint Variation

Lear;ing Target:I can write and apply direct, inverse,

and joint variation models and solve real-life problems. [A.CED.2]

Variations - special relationships between variables k = constant variation

"y varies directly with x" "y is directly proportional to x"

Example:

Imagine you make $10 per hour. What happens to your pay if you work more hours? less hours?

Direct variation y = kx

• as one variable _____, the other variable _____ • the ratio between the variables stays constant.

We use direct variation in situations where:

"y varies inversely with x" "y is inversely proportional to x:

xky =

Inverse variation

4 people can paint a fence in 3 hours. If more people help paint, will it take more or less time? (Assume everyone works at the same rate.)

Example:

• as one variable _____, the other variable ______ • the product of the variables stays constant.

We use inverse variation for situations where:

Joint variation

Example:

Recall in geometry that the volume of a pyramid is V = Bh where B is base area and h is the height. What happens to the volume of a pyramid as the base area AND the height increase?

13

"y varies jointly with x and z" "y varies directly with x and z"

y = kxz (varies directly as product of variables)

1. Write an equation for the given relationship.

b) y varies jointly with z and the square root of x.

c) w varies inversely with x and jointly with y and z.

a) m varies inversely with the cube of t.

Classify the following as direct, inverse, joint or no variation.

2. a = 7b

4. y = x + 3

3. 4de = g

5. cd

= 8

6. y varies directly with x. If y = 8 when x = 3, find y when x = – 4

7. y varies inversely with x. If y = 6 when x = 2, find y when x = 10.

Write an equation relating the variables, then find the missing variable:

equation: ______________ y = ____

equation: ______________ y = ____

8. z varies jointly with x and y. If x = 3, y = 8, z = 6, find z when x = – 4 and y = 7.

equation: ______________ z = ____

9. m is inversely proportional to the square root of n. If m = 27 and n = 16, find m when n = 64.

equation: ______________ m = ____

The force F needed to loosen a bolt with a wrench varies inversely with the length L of the handle. Write an equation relating F and L, given that 250 pounds of force must be exerted to loosen a bolt when using a wrench with a handle 6 inches long. How much force must be exerted when using a wrench with a handle 24 inches long?

10.

equation: ______________ force = ____

Assignment: 9.1 wksht

Answers to 9.1 WS

y=km√b

y = kx2

w = kx yz w = kyzxor

a = kcd

y = -2x 12

-128

12

y = 640x

y = 60x

p = 35 qr3

r = x212 32

z = xy124

12

625

6 amperes

160 cm3

$384