The document discusses direct and inverse variation problems. It provides examples of how to solve each type of problem. For a direct variation problem, a constant k is determined using given values for variables x and y. Then k is used to find the value of y when a new value of x is given. For an inverse variation problem, a constant k is similarly determined using given values for variables that have an inverse relationship, like supply (S) and demand (D). Then k is used to find the value of the variable when a new value of the related variable is given.

1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
2
Rational
Expressions and
Applications
14

2. Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
1. Solve direct variation problems.
2. Solve inverse variation problems.
Objectives
7.8 Variation

3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Direct Variation
y varies directly as x if there exists a constant k
such that
y = kx.
Solve Direct Variation Problems

4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Example
Suppose y varies directly as x, and y = 600 when x = 12.
Find y when x = 25.
Solve Direct Variation Problems
The first part of the problem gives us the information we need to
find the constant k. Then, we can find y when x = 25.
Since y varies directly as x,
y = kx
600 = k · 12
50 = k
Now we can solve for y.
y = 50x
y = 50 · 25
y = 1250

5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
.
k
y
x
Inverse Variation
y varies inversely as x if there exists a constant k
such that
Solve Inverse Variation Problems

6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Example
At one Toys R Us store, the supply and demand for the latest
singing stuffed animal have an inverse relationship. When the
manufacturer supplies 500 stuffed animals, the demand is for
4000. Find the demand when the manufacturer supplies the
store with 2000 stuffed animals.
Solve Inverse Variation Problems
Let D = # of stuffed animals demanded, and
S = # of stuffed animals supplied.
Since supply and demand have an inverse relationship,
.
k
D
S


7. Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
500
 
  
 
Use D = 4000 and S = 500. Solve for D when S = 2000.
The first part of the problem gives us the information we need to
find the constant k. Then we can find D when S = 2000.
Example (concluded)
Solve Inverse Variation Problems
4000
500
k
 500
2,000,000 = k
2,000,000
D
S

2,000,000
2000
D 
1000D 
When the manufacturer supplies the store with 2000
stuffed animals, the demand is for 1000.