Inverse Variation

1
Inverse Variation
ALGEBRA 1 LESSON 8-10
(For help, go to Lesson 5-5.)
Suppose y varies directly with x. Find each
constant of variation. 1. y 5x 2. y 7x 3. 3y
x 4. 0.25y x Write an equation of the direct
variation that includes the given point. 5. (2,
4) 6. (3, 1.5) 7. (4, 1) 8. (5, 2)
8-10
2
Inverse Variation
ALGEBRA 1 LESSON 8-10
1. y 5x constant of variation 5 2. y 7x
constant of variation 7 3. 3y x
3y x y x constant of
variation 4. 0.25y x y x 4
y 4 x y 4x constant of
variation 4
Solutions
1 3
1 3
1 3
1 3
1 4
1 4
8-10
3
Inverse Variation
ALGEBRA 1 LESSON 8-10
Solutions (continued)
5. Point (2, 4) in y kx 4 k(2), so k 2
and y 2x. 6. Point (3, 1.5) in y kx 1.5
k(3), so k 0.5 and y 0.5x. 7. Point (4, 1)
in y kx 1 k(4), so k and y
x. 8. Point (5, 2) in y kx 2 k(5), so k
and y x.
1 4
1 4
2 5
2 5
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4
Inverse Variation
ALGEBRA 1 LESSON 8-10
Suppose y varies inversely with x, and y 9
when x 8. Write an equation for the inverse
variation.
xy k Use the general form for an inverse
variation.
(8)(9) k Substitute 8 for x and 9 for y.
72 k Multiply to solve for k.
xy 72 Write an equation. Substitute 72 for k in
xy k.
8-10
5
Inverse Variation
ALGEBRA 1 LESSON 8-10
The points (5, 6) and (3, y) are two points on
the graph of an inverse variation. Find the
missing value.
x1 y1 x2 y2 Use the equation x1 y1 x2
y2 since you know coordinates, but not the
constant of variation.
5(6) 3y2 Substitute 5 for x1, 6 for y1, and 3
for x2.
30 3y2 Simplify.
10 y2 Solve for y2.
The missing value is 10. The point (3, 10) is on
the graph of the inverse variation that includes
the point (5, 6).
8-10
6
Inverse Variation
ALGEBRA 1 LESSON 8-10
Jeff weighs 130 pounds and is 5 ft from the
levers fulcrum. If Tracy weighs 93 pounds, how
far from the fulcrum should she sit in order to
balance the lever?
8-10
7
Inverse Variation
ALGEBRA 1 LESSON 8-10
(continued)
650 93x Simplify.
Tracy should sit 6.99, or 7 ft, from the fulcrum
to balance the lever.
8-10
8
Inverse Variation
ALGEBRA 1 LESSON 8-10
Decide if each data set represents a direct
variation or an inverse variation. Then write an
equation to model the data.
The values of y seem to vary inversely with the
values of x.
The product of xy is the same for all pairs of
data.
So, this is an inverse variation, and k 30.
The equation is xy 30.
8-10
9
Inverse Variation
ALGEBRA 1 LESSON 8-10
(continued)
The values of y seem to vary directly with the
values of x.
So, this is a direct variation, and k 1.5.
The equation is y 1.5x.
8-10
10
Inverse Variation
ALGEBRA 1 LESSON 8-10
Explain whether each situation represents a
direct variation or an inverse variation.
a. You buy several souvenirs for 10 each.
The cost per souvenir times the number of
souvenirs equals the total cost of the souvenirs.
b. The cost of a 25 birthday present is split
among several friends.
The cost per person times the number of people
equals the total cost of the gift.
Since the total cost is a constant product of
25, this is an inverse variation.
8-10
11
Inverse Variation
ALGEBRA 1 LESSON 8-10
1. The points (5, 1) and (10, y) are on the graph
of an inverse variation. Find y. 2. Find the
constant of variation k for the inverse variation
where a 2.5 when b 7.
0.5
17.5
3. Write an equation to model the data and
complete the table.
4. Tell whether each situation represents a
direct variation or an inverse variation. a. You
buy several notebooks for 3 each. b. The 45
cost of a dinner at a restaurant is split among
several people.
direct variation
Inverse variation
8-10