A2 – Section 8.1
Date____________
Variation
Variations: describe how two or more variables are related using only _____________
or ______________.
Types:
Direct:______________
Inverse:_____________
Joint:_______________
Constant of Variation: _____, a non-zero constant.
Using variations:
1. Recognize the __________ of variation.
2. Find the constant of variation, ______.
3. Write an equation that relates the ____________________.
4. Use the _______________ of variation.
Ex 1 Does the equation represent a direct variation, inverse variation or neither?
y
x
a)
xy = 4.8
b)
c)
y= -3x + 1
1 .5
a)_____________
b)_____________
Ex 2 x and y vary inversely. Y = 6 when x = 1.5.
a)
Write the equation of variation.
b)
c)______________
Find y when x = 4/3
Ex 3 Does the data show an inverse variation or a direct variation? Find the model.
W 2 4
6 8
10
H
9 4.5 3 2.25 1.8
Model?
Writing equations of variations
1.
K is always in the _______________
2.
The variable before the phrase ‘varies’ equals the other parts of the sentence.
3.
Direct variation – all variables are in the _____________
Inverse variation – there will be a __________________
Ex 4 Write an equation to describe the variation.
_______________a) Y varies directly with x and inversely with z2.
_______________b) Y varies inversely with x3.
_______________c) Z varies jointly with x2 and y.
_______________d) Y varies inversely with x and z.
Ex 5 The volume of gas in a container varies inversely with the amount of pressure. A
gas has a volume of 75 in3 at a pressure of 25 lb/in2. Write a model relating volume and
pressure.