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