IDENTIFYING INVERSE VARIATION FROM AN EQUATION:
Ask yourself the question:
9­1 A
INVERSE VARIATION
EX1
Objective: To write and interpret inverse variation problems.
Inverse Variation = when two variables have a constant relationship
x = independent variable
y = dependent variable
k = constant of variation
Equation:
EX2
How do we read it?
"y varies inversely with x"
"y varies inversely as x"
"y is inversely proportional to x"
EX3
Whatever the y variable represents comes before the word "inversely".
Whatever the x variable represents comes after the word "inversely".
EX1
"n varies inversely with m" is written as: Can we re­write the equation as
?
IDENTIFYING INVERSE VARIATION FROM A TABLE:
WRITE AN EQUATION FOR INVERSE VARIATION:
If we start with the equation...
When given a pair of x and y values (an ordered pair):
and solve for k...
EX1
EX2
EX3
x
y
3
8
6
4
12
2
x
y
1
2
2
1
3
0.5
x
y
0.5
18
2
4.5
6
1.5
EX1
Write an inverse variation model for
EX2
Suppose you have an inverse variation relationship that passes through the point (4,8). Write an equation for that relationship.
EX3
If y varies inversely with x and passes through the point (5,2), model that relationship.
x = 5 and y = 3
xy
xy
xy
FINDING A MISSING VALUE:
We have two methods for doing this. You may choose the method that makes more sense to you.
If there is an inverse relationship, find the missing value:
( 3, 4 ) and ( 6, y )
Method #1:
Use the complete ordered pair to find the value of k first.
USING INVERSE VARIATION TO SOLVE "REAL WORLD" PROBLEMS:
A group of college students rents a large two­story house. The amount of rent (r) in dollars that each student pays is inversely proportional to the number of students (n) sharing the house.
If there are 5 students each paying $240 in rent each month, write a model for the situation.
Method #2: Use a generic inverse variation equation and solve for k.
Then set k1 = k2.