Inverse VariationsLesson 11-6

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

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.)

Writing an Equation For an Inverse Variation, given a Point

xy =k(3)(8) =k

24=k

xy = 24 or

B. 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

USING INVERSE VARIATION:

C. 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

________________________ = ________________

_______________ = ________________

_______________ = ________________

1000(7)160 d

160 d 7,000

d = 43.75 ft

D. 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?

80(d)(120)(5) =

600 = 80d

7.5 ft. = d

weight1 ● distance 1 = weight 2 ● distance 2

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

x –8 –4 –2 –1 0 1 2 4 8

y 1 2 4 8 undefined -8 -4 -2 -1

F. Graph the equation xy = –8

y = ___________

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

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

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

G. 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

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

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 = 14.99 ● n

Since this is in the form of y = kx, this is a direct variation.