Post on 22-Feb-2016
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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.