Inverse Variation

1. Section 6-9
Inverse Variation

2. Essential Question
How do you solve problems involving
inverse variation and inverse square
variation functions?
Where you’ll see this:
Music, physics, industry, travel

3. Vocabulary
1. Inverse Variation:
2. Inverse Square Variation:

4. Vocabulary
1. Inverse Variation: A variation situation where
when one variable gets larger, the other gets
smaller
2. Inverse Square Variation:

5. Vocabulary
1. Inverse Variation: A variation situation where
when one variable gets larger, the other gets
smaller
2. Inverse Square Variation: An inverse variation
situation where the independent variable is
squared

6. Inverse Variation Function:
Inverse Square Variation Function:

7. Inverse Variation Function:
k
y=
x
Inverse Square Variation Function:

8. Inverse Variation Function:
k
y=
x
k ≠ 0, x ≠ 0
Inverse Square Variation Function:

9. Inverse Variation Function:
k
y=
x
k ≠ 0, x ≠ 0
Inverse Square Variation Function:
k
y= 2
x

10. Inverse Variation Function:
k
y=
x
k ≠ 0, x ≠ 0
Inverse Square Variation Function:
k
y= 2
x
k ≠ 0, x ≠ 0

11. Example 1
The force of gravitational attraction between two
objects varies inversely as the distance between
them. If two objects have a gravitational force of
550 newtons (N) when they are 2200 m apart, how
far apart are they when their gravitational force is
665.5 N?

12. Example 1
The force of gravitational attraction between two
objects varies inversely as the distance between
them. If two objects have a gravitational force of
550 newtons (N) when they are 2200 m apart, how
far apart are they when their gravitational force is
665.5 N?

13. Example 1
The force of gravitational attraction between two
objects varies inversely as the distance between
them. If two objects have a gravitational force of
550 newtons (N) when they are 2200 m apart, how
far apart are they when their gravitational force is
665.5 N?
force distance

14. Example 1
The force of gravitational attraction between two
objects varies inversely as the distance between
them. If two objects have a gravitational force of
550 newtons (N) when they are 2200 m apart, how
far apart are they when their gravitational force is
665.5 N?
y = force x = distance

15. Example 1
The force of gravitational attraction between two
objects varies inversely as the distance between
them. If two objects have a gravitational force of
550 newtons (N) when they are 2200 m apart, how
far apart are they when their gravitational force is
665.5 N?
y = force x = distance
k
y=
x

16. Example 1
y = force x = distance
k
y=
x

17. Example 1
y = force x = distance
k
y=
x
k
550 =
2200

18. Example 1
y = force x = distance
k
y=
x
k
550 =
2200
k = 1210000

19. Example 1
y = force x = distance
k 1210000
y= y=
x x
k
550 =
2200
k = 1210000

20. Example 1
y = force x = distance
k 1210000
y= y=
x x
k 1210000
550 = 665.5 =
2200 x
k = 1210000

21. Example 1
y = force x = distance
k 1210000
y= y=
x x
k 1210000
550 = 665.5 =
2200 x
k = 1210000 665.5x = 1210000

22. Example 1
y = force x = distance
k 1210000
y= y=
x x
k 1210000
550 = 665.5 =
2200 x
k = 1210000 665.5x = 1210000
2
x = 1818
11

23. Example 1
y = force x = distance
k 1210000
y= y=
x x
k 1210000
550 = 665.5 =
2200 x
k = 1210000 665.5x = 1210000
2
x = 1818 m
11

24. Example 2
The weight of a body is inversely proportional to
the square of its distance from the center of the
Earth. If a man weighs 147 lb on Earth’s surface,
what will he weight 200 miles above Earth?
(Assume Earth’s radius to be 4000 mi.)

25. Example 2
The weight of a body is inversely proportional to
the square of its distance from the center of the
Earth. If a man weighs 147 lb on Earth’s surface,
what will he weight 200 miles above Earth?
(Assume Earth’s radius to be 4000 mi.)

26. Example 2
The weight of a body is inversely proportional to
the square of its distance from the center of the
Earth. If a man weighs 147 lb on Earth’s surface,
what will he weight 200 miles above Earth?
(Assume Earth’s radius to be 4000 mi.)
weight distance

27. Example 2
The weight of a body is inversely proportional to
the square of its distance from the center of the
Earth. If a man weighs 147 lb on Earth’s surface,
what will he weight 200 miles above Earth?
(Assume Earth’s radius to be 4000 mi.)
y = weight x = distance

28. Example 2
The weight of a body is inversely proportional to
the square of its distance from the center of the
Earth. If a man weighs 147 lb on Earth’s surface,
what will he weight 200 miles above Earth?
(Assume Earth’s radius to be 4000 mi.)
y = weight x = distance
k
y= 2
x

29. Example 2
y = weight x = distance
k
y= 2
x

30. Example 2
y = weight x = distance
k
y= 2
x
k
147 = 2
4000

31. Example 2
y = weight x = distance
k
y= 2
x
k
147 = 2
4000
k
147 =
16000000

32. Example 2
y = weight x = distance
k
y= 2
x
k
147 = 2
4000
k
147 =
16000000
k = 2352000000

33. Example 2
y = weight x = distance
k 2352000000
y= 2 y= 2
x x
k
147 = 2
4000
k
147 =
16000000
k = 2352000000

34. Example 2
y = weight x = distance
k 2352000000
y= 2 y= 2
x x
k 1210000
147 = 2
y= 2
4000 4200
k
147 =
16000000
k = 2352000000

35. Example 2
y = weight x = distance
k 2352000000
y= 2 y= 2
x x
k 1210000
147 = 2
y= 2
4000 4200
k 2352000000
147 = y=
16000000 17640000
k = 2352000000

36. Example 2
y = weight x = distance
k 2352000000
y= 2 y= 2
x x
k 1210000
147 = 2
y= 2
4000 4200
k 2352000000
147 = y=
16000000 17640000
k = 2352000000 1
y = 133
3

37. Example 2
y = weight x = distance
k 2352000000
y= 2 y= 2
x x
k 1210000
147 = 2
y= 2
4000 4200
k 2352000000
147 = y=
16000000 17640000
k = 2352000000 1
y = 133 lb
3

38. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.

39. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k
y=
x

40. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k
y=
x
k
15 =
10

41. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k
y=
x
k
15 =
10
k = 150

42. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k 150
y= y=
x x
k
15 =
10
k = 150

43. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k 150
y= y=
x x
k 150
15 = y=
10 5
k = 150

44. Example 3
Assume y varies inversely as x.
a. When x = 10, y = 15. Find y when x = 5.
k 150
y= y=
x x
k 150
15 = y=
10 5
k = 150 y = 30

45. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.

46. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k
y=
x

47. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k
y=
x
k
10 =
2

48. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k
y=
x
k
10 =
2
k = 20

49. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k 20
y= y=
x x
k
10 =
2
k = 20

50. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k 20
y= y=
x x
k 20
10 = y=
2 40
k = 20

51. Example 3
Assume y varies inversely as x.
b. When x = 2, y = 10. Find y when x = 40.
k 20
y= y=
x x
k 20
10 = y=
2 40
k = 20 1
y=
2

52. Problem Set

53. Problem Set
p. 284 #1 - 21 odd
"If people only knew how hard I work to gain my
mastery, it wouldn't seem so wonderful at all."
- Michelangelo Buonarroti