5.6 Inverse Variations
inverse variation -
note: y varies indirectly with x
an equation in the form x y = k, where k = 0
Inverse variations have graphs with the same general
shape. You can see from the graph at the right how
the constant of variation, 'k' affects the graph x y = k.
Let's compare:
Find the constant of variation (k) for each inverse variation:
x1 y1 = x 2 y2
Each pair of points is on a graph of an inverse variation. Find
the missing value.
(100, 2) and (2, y)
(x, 4) and(5, 6)
(6, 1) and (x, -2)
(8, y) and (-2, 4)
(3, 6) and (9, y)
You try:
Jeff weighs 130 pounds and is 5 ft from the
lever's fulcrum. If Tracy weighs 93 pounds,
how far from the fulcrum should she sit in
order to balance the lever?
R:
D:
W:
Compare . . .
Decide whether each set of data represents a direct variation or an
inverse variation. Then write an equation to model the data.
Direct or Indirect (inverse) that is the question . . .
Determine whether each situation is a direct or indirect
variation. Then write a rule and answer the question.
Two rectangular fields
have the same area. One
measures 75 yds. by 60
yds. If the other field has
a length of 72 yds, what is
its width?
R:
D:
W:
The perimeter of a square
depends on the length of its side.
What is the perimeter of a square
with side length of 13.4 cm?
R:
D:
W:
R:
D:
W:
After 30 minutes a car
moving at a constant speed
has traveled 25 miles.
Moving at the same speed,
how far will it travel in 140
minutes?