Name———————————————————————— Lesson
5.1
Date —————————————
Practice B
For use with the lesson “Model Inverse and Joint Variation”
Tell whether x and y show direct variation, inverse variation, or neither.
3
3. x 5 ​ } ​
y
x
2. y 5 ​ } ​
3
1. y 5 2x 1 3
1
4.​ } ​ xy 5 2
2
Lesson 5.1
The variables x and y vary inversely. Use the given values to write an
equation relating x and y. Then find y when x 5 0.5.
5. x 5 4, y 5 6
5
6. x 5 2, y 5 ​ } ​
2
8. x 5 23, y 5 2
3
4
9. x 5 ​ } ​, y 5 }
​ 2 ​
3
1
7. x 5 48, y 5 ​ }  ​ 
12
1
1
10. x 5 ​ } ​, y 5 }
​ 3 ​
2
Determine whether x and y show direct variation, inverse variation,
or neither.
11.
x
1
2
3
4
y
1
4
9
16
12.
x
2
5
8
15
y
60
24
15
8
13.
x
1
4
7
10
y
7.5
30
52.5
75
14. x 5 3, y 5 5, z 5 30
1
15. x 5 6, y 5 ​ } ​, z 5 24
2
3
16. x 5 ​ } ​, y 5 18, z 5 9
2
In Exercises 17–20, use the following information.
Simple Interest The simple interest I (in dollars) for a savings account is jointly
proportional to the product of the time t (in years) and the principal P (in dollars).
After fifteen months, the interest on a principal of $2500 is $78.13.
17. Find the constant of variation k.
18. Write an equation that relates I, t, and P.
19. What will the interest I be after ten years?
20. What does the constant of variation k represent?
In Exercises 21–23, use the following information.
Boyle’s Law Boyle’s Law states that for a constant temperature, the pressure p of a
gas varies inversely with its volume V. A sample of oxygen gas has a volume of
50.25 cubic milliliters at a pressure of 20.6 atmospheres.
21. Find the constant of variation k.
22. Write an equation that relates p and V.
23. Find the volume of the oxygen gas if the pressure changes to 15.2 atmospheres.
5-6
Algebra 2
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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 5 4 and y 5 7.
Answers for Chapter 5
Lesson 5.1 Model Inverse and
Joint Variation
43725
14. 10 yr 15. 43,725 16. d 5 }
​  p   
 
​
Teaching Guide
19. 4.541 kilocalories
1. Divide distance by speed traveled; 4 h;
about 4 h 44 min 2. Sample answer: speed
Study Guide
Practice Level A
1. direct variation 2. neither 3. inverse
variation 4. inverse variation
6
15 15
212
5. y 5 }
​ x ​; 3 6. y 5 }
​  x  ​; }
​ 2  ​ 7. y 5 }
​  x   
 ​; 26
16
3 3
6
8. y 5 }
​  x  ​; 8 9. y 5 }
​ x ​; ​ }2 ​ 10. y 5 }
​ x ​; 3
11. direct variation 12. neither 13. inverse
variation 14. neither 15. direct variation
16. inverse variation 17. z 5 4xy; 40
1
18. z 5 2xy; 20 19. z 5 }
​ 2 ​ xy; 5 20. 0.04
21. I 5 0.04tP 22. $240 23. The interest rate
17. 7950 units 18. 0.22; H 5 0.22mT
15
1. inverse 2. neither 3. direct 4. y 5 }
​  x  ​; 5
12
2 2
5. y 5 }
​  x  ​; 4 6. y 5 }
​ x ​; ​ }3 ​ 7. about 231 8. 36
Problem Solving Workshop:
Using Alternative Methods
1. about 347 2. about 93 mm2
Challenge Practice
1. False. y will decrease because y and x are
inversely related.
a
2. True. If y 5 }
​  2  ​and x is replaced with 2x, you
x
a
a
   ​ 5 }
​   2 ​. 
have y 5 ​ }
(2x)2
4x
3. True. If y varies directly with x, then y 5 ax,
1
of the savings account.
so x 5 ​ }a ​ y. So, x varies directly with y.
Practice Level B
4. False. z will decrease when y > 0 and z will
increase when y < 0. 5. w varies jointly with x
and y, and inversely with the square root of z.
1. neither 2. direct variation 3. inverse
variation 4. inverse variation
5
24
4
5. y 5 }
​  x  ​; 48 6. y 5 }
​ x ​; 10 7. y 5 }
​ x ​; 8
26
2
1 1
8. y 5 }
​  x    ​; 212 9. y 5 }
​ x ​; 4 10. y 5 }
​ 6x  ​; }
​ 3 ​
}
1 w​Ï z ​ 
   
​  ; x varies jointly with w and the
x 5 ​ } ​p ​ }
a
y
square root of z, and inversely with y.
1
}
w​Ï z ​ 
y 5 ​ }a ​p ​ }
   
 ​ ; y varies jointly with w and the
x
11. neither 12. inverse variation 13. direct
variation 14. z 5 2xy; 56 15. z 5 8xy; 224
square root of z, and inversely with x.
28
1
16. z 5 }
​ 3 ​ xy; }
​ 3  ​ 17. 0.025 18. I 5 0.025tP
z 5 a2 p }
​  2   ​ ; z varies jointly with the squares of
19. $625 20. The interest rate of the savings
account 21. 1035.15
x and y, and inversely with the square of w.
1035.15
22. V 5 }
​  p   
 
​ 23. 68.1 mL3
Practice Level C
1. direct variation 2. neither 3. inverse
variation 4. inverse variation
8.64
15
5. y 5 }
​  x   
 ​; 34.56 6. y 5 }
​  x  ​; 60
5
7. y 5 }
​ 8x  ​; 2.5 8. direct variation 9. neither
answers
decreases; time traveled increases; time will
increase as speed decreases
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Rational Functions
x 2y 2
w
6. t varies directly with u, and inversely with the
1
square of v and with w. u 5 ​ }a ​p tv 2w; u varies
jointly
with t, with the square of v, and with w.
}
​Ïu ​ 
​  } 
 ​; v varies directly with the
v5Ï
​ a ​ p }
​
Ï​ tw  
}
square root of u, and inversely with the square
u
tv
10. inverse variation 11. z 5 18xy; 540
roots of t and w. w 5 a p }
​  2    ​; w varies
15
25
125
12. z 5 }
​ 2  ​ xy; 225 13. z 5 }
​ 84 ​ xy; }
​ 14  ​
directly with u, and inversely with t and the square
of v.
Algebra 2
Chapter Resource Book
A1