1. Inverse Variations
Lesson 11-6

2. xy =k k product xy =k (3)(8) =k 24=k xy = 24
An equation in the form of ____________________ or ____________ is an inverse variation,. The constant of variation is _______, the _______________ of x and y for an ordered pair (x, y) that solves the inverse variation.
xy =k k
product
Writing an Equation For an Inverse Variation, given a Point
A Suppose y varies inversely with x, and y = 8, when x = 3. What is an
equation for the inverse variation?
_______________ (the general form of an inverse variation)
_______________ (Substitute known values)
_______________ (simplify)
_______________ (Write the equation.)
xy =k
(3)(8) =k
24=k
xy = 24 or

3. Suppose y varies inversely with x, and y = 9 when x = 6
Suppose y varies inversely with x, and y = 9 when x = 6. What is an equation
for the inverse variation?
_______________ (the general form of an inverse variation)
_______________ (Substitute known values)
_______________ (simplify)
_______________ (Write the equation.)
xy =k
(6)(9) =k
54=k
xy = 54 or

4. USING INVERSE VARIATION:
The weight needed to balance a lever varies inversely with the distance from
the fulcrum to the weight. How far away would a 160 pound person have to be to balance a 1000 pound elephant that is 7 feet away from the fulcrum?
weight1 ● distance 1 = weight 2 ● distance 2
________________________ = ________________
_______________ = ________________
_______________ = ________________
160 d
1000(7)
160 d
7,000
d = ft

5. A 120-pound weight is placed on a lever, 5 feet from the
fulcrum. How far away from the fulcrum should an 80-pound weight be placed to balance the lever?
weight1 ● distance 1 = weight 2 ● distance 2
(120)(5) =
80(d) =
80d
7.5 ft. = d

6. -1 -2 -4 -8 8 4 2 1
Und.

7. Graph the equation xy = –8 y = ___________ x –8 –4 –2 –1 1 2 4 8 y -8 1 2 4 8 y
undefined -8 -4 -2 -1

8. Graph must pass through origin (0,0) and is a straight line.

9. The constant (k) is equal to the product of x and y (k=xy).

10. Determining Direct or Inverse Variation
To determine if a table or set of data is a direct variation, check each ratio . .
If they are constant, then it is a direct variation with the equation y = kx or
If it is not a direct variation, check the product of xy and see if that is constant. If it is, you have an inverse variation with the equation xy = k or
Determine if the table represents a direct variation or an inverse variation.
Write an equation for the table.  
Since the ratio is constant (-5), this is a direct variation. The equation is y = 5x

11. Check the ratio of y/x to see if it is a direct variation.
Since 4.5 ≠ 1.125, this is not a direct variation.
Check the product of xy to see if this is an inverse variation.
(2)(9) = 18
(4)(4.5) = 18
(6)(3) = 18
Since the product of xy is constant, this is an inverse variation. The equation is xy = 18 or

12. Direct or Inverse Variation: Real-World Examples
I. The cost of a $120 boat rental is split among several friends.
Does this represent an example of a direct variation or an
inverse variation?
J. You download several movies for $14.99 each. Is this an example
of a direct variation or an inverse variation?
Write an equation to model the situation:
Cost per person times the number of people = boat rental
c ● n = 120
Since this is in the form of xy=k, this is an inverse variation.
Write an equation to model the situation:
Total cost = Cost per movie times the number of movies
C = ● n
Since this is in the form of y = kx, this is a direct variation.