Algebra II
Unit 8 Day 5 - Variation
Name _______________________
Date ____________ Block ______
Direct Variation:
Inverse Variation:
Joint Variation:
k
y=
z = kxy
x
(k is the constant of variation and cannot be zero)
y = kx
“y varies directly with x”
“y varies inversely with x”
“z varies jointly with x and y”
Tell whether x and y show direct variation, inverse variation, or neither.
2
1. y = 3x
2. y =
3. x + y = 7
x
1. ___________
2. _____________
4. xy = 5
3. _____________
4. _____________
The variables x and y vary inversely. Use the given values to write an equation relating x and y.
Then find y when x = 4 for each problem.
5. x = 2, y = 4
6. x = -4, y = 9
7. x = 10, y = ½
5. equation: ___________
y = _____
6. equation: ___________
y = ______
7. equation: ___________
y = ______
Determine whether x and y show direct variation, inverse variation, or neither.
8.
9.
10.
y
x
y
x
y
3
12
1
6
3
1
8
11
32
44
2
4
5
3
6
10
0.5
0.3
0.5
2
5
2
12
0.25
x
8. ____________
9. ____________
10. ____________
The variable z varies jointly with x and y. Use the given values to write an equation relating
x, y, and z. Then find z when x = -3 and y = 4.
11. x = 1, y = 2, z = 6
12. x = 2, y = 3, z = 4
13. x = 4, y = 3, z = 24
11. equation: _________
z = ______
12. equation: __________
z = ______
13. equation: ___________
z = ______
Write an equation for the given relationship.
14. y varies directly with x __________
15. y varies inversely with x __________
16. z varies jointly with x and y __________
17. y varies inversely with the square of x _______
18. z varies directly with x and inversely with y __________
Applications: Complete each problem.
19. The volume of a gas in a container varies inversely with the amount of pressure. A gas has a volume of
75 in3 at a pressure of 25 lb/in2. Write a model relating the volume and pressure.
19. ____________________________
20. The force F needed to loosen a bolt with a wrench varies inversely with the length l of the handle.
a) Write an equation relating F and l, given that 250 pounds of force must be exerted to loosen a bolt
when using a wrench with a handle 6 inches long. b) How much force must be exerted when using a
wrench with a handle 24 inches long?
20. a) equation:_______________________
b) ____________________________
21. The volume of a geometric figure varies jointly with the square of the radius of the base and the
height. a) Write an equation for the volume. b) Estimate the constant of variation if V = 63.33in3,
r = 2.4 in, and h = 10.5 in.
21. a) equation:_______________________
b) ___________________________
22. If a basketball team’s present record is 42 wins and 36 losses, how many consecutive games must it
win so that its winning record reaches 60%?
22. ______________________________
Solve each problem.
6
23.
= -2
x-5
23. _________________
26.
3x + 8
= 21
x+5
26. _________________
24. 12 =
x-8
x+3
25.
24. __________________
27.
2 =
2x + 14
x-1
REVIEW: Perform the indicated operations and simplify the results.
x2  x  12
x2  25
29.
30.
2
2
x  8x  15
x  6x  5
32.
5x2  6x  1 2x  18

9x  81
10x  2
34.
4
9

a 3 a 5
33.
35.
x+4
x-3
25. _________________
28.
27. __________________
8=
0.4 =
5x - 4
10x - 3
28. _________________
31.
x2  4
4

8x2  16x x2  x
x 2
4x2
x
 2
 2
8x  4 x  2x 6x  3x
1
1
5


x  2 x  3 x2  x  6
HOMEWORK Day 64 pg. 590 – 591 #7 – 20 all, #23 – 28 all
COPY EACH PROBLEM ON CLEAN PAPER AND SHOW ALL WORK!