DATE
NAME
4-8
Student Edition
Pages 239–244
Study Guide
Direct and Inverse Variation
If two variables x and y are related by the equation y 5 kx,
where k is a nonzero constant, then the equation is called a
direct variation, and k is called the constant of variation.
If two variables x and y are related by the equation xy 5 k,
where k Þ 0, then the equation is called an inverse variation.
Example 1: If y varies directly as x, and
y 5 12 when x 5 4, find y
when x 5 7.
y 5 kx
y 5 kx
y 5 3(7)
12 5 4k
12
4
u
4k
5 4
35k
Example 2: If y varies inversely as x, and
y 5 3 when x 5 12, find x
when y 5 4.
xy 5 k
xy 5 k
12(3) 5 k
4x 5 36
y 5 21
36 5 k
u
4x
4
36
5 4
x59
Solve. Assume that y varies directly as x.
1. If y 5 4 when x 5 2, find y
when x 5 16.
2
2. If y 5 9 when x 5 23, find x
when y 5 6.
1
1
3. If y 5 5 when x 5 3 , find y
1
when x 5 4.
1
4. If y 5 4 when x 5 8 , find x
3
when y 5 16 .
Solve. Assume that y varies inversely as x.
5. If y 5 9 when x 5 7, find y
when x 5 2.
1
1
7. If x 5 2 when y 5 3 , find y
1
when x 5 4.
© Glencoe/McGraw-Hill
6. If y 5 4.3 when x 5 12.9, find y
when x 5 15.8.
1
8. If y 5 26 when x 5 4, find y
3
when x 5 16 .
33
Algebra 1
DATE
NAME
4-8
Student Edition
Pages 239–244
Practice
Direct and Inverse Variation
Solve. Assume that y varies directly as x.
1. If y 5 24 when x 5 2, find y when
x 5 26.
2. If y 5 16 when x 5 4, find y when
x 5 6.
3. If y 5 25 when x 5 12.5, find x when
y 5 15.
4. If y 5 7 when x 5 4, find y when
x 5 12.
5. If y 5 80 when x 5 32, find x when
y 5 100.
6. If y 5 198 when x 5 22, find y when
x 5 182.
7. If y 5 28 when x 5 168, find y when
x 5 108.
8. If y 5 24 when x 5 6, find y when
x 5 24.
Solve. Assume that y varies inversely as x.
9. If y 5 24 when x 5 2, find y when
x 5 26.
10. If y 5 16 when x 5 4, find y when
x 5 6.
11. If y 5 25 when x 5 12.5, find x when
y 5 15.
12. If y 5 7 when x 5 4, find y when
x 5 12.
13. If y 5 27 when x 5 12, find x when
y 5 212.
14. If y 5 6 when x 5 24, find x when
12
y5 5.
15. If y 5 60 when x 5 80, find x when
y 5 220.
16. If y 5 40 when x 5 16, find y when
x 5 10.
© Glencoe/McGraw-Hill
33
Algebra 1
DATE
NAME
4-8
Student Edition
Pages 239–244
Study Guide
Direct and Inverse Variation
If two variables x and y are related by the equation y 5 kx,
where k is a nonzero constant, then the equation is called a
direct variation, and k is called the constant of variation.
If two variables x and y are related by the equation xy 5 k,
where k Þ 0, then the equation is called an inverse variation.
Example 1: If y varies directly as x, and
y 5 12 when x 5 4, find y
when x 5 7.
y 5 kx
y 5 kx
y 5 3(7)
12 5 4k
12
4
u
4k
5 4
35k
Example 2: If y varies inversely as x, and
y 5 3 when x 5 12, find x
when y 5 4.
xy 5 k
xy 5 k
12(3) 5 k
4x 5 36
y 5 21
36 5 k
u
4x
4
36
5 4
x59
Solve. Assume that y varies directly as x.
1. If y 5 4 when x 5 2, find y
when x 5 16.
2. If y 5 9 when x 5 23, find x
when y 5 6.
22
32
2
1
1
3. If y 5 5 when x 5 3 , find y
1
when x 5 4.
1
4. If y 5 4 when x 5 8 , find x
3
when y 5 16 .
3
10
3
32
Solve. Assume that y varies inversely as x.
5. If y 5 9 when x 5 7, find y
when x 5 2.
6. If y 5 4.3 when x 5 12.9, find y
when x 5 15.8.
63
2
5547
1580
1
1
1
7. If x 5 2 when y 5 3 , find y
1
when x 5 4.
8. If y 5 26 when x 5 4, find y
3
when x 5 16 .
2
3
© Glencoe/McGraw-Hill
28
T33
Algebra 1
DATE
NAME
4-8
Student Edition
Pages 239–244
Practice
Direct and Inverse Variation
Solve. Assume that y varies directly as x.
1. If y 5 24 when x 5 2, find y when
x 5 26. 12
2. If y 5 16 when x 5 4, find y when
x 5 6. 24
3. If y 5 25 when x 5 12.5, find x when
y 5 15. 237.5
4. If y 5 7 when x 5 4, find y when
x 5 12. 21
5. If y 5 80 when x 5 32, find x when
y 5 100. 40
6. If y 5 198 when x 5 22, find y when
x 5 182. 1638
7. If y 5 28 when x 5 168, find y when
x 5 108. 18
8. If y 5 24 when x 5 6, find y when
x 5 24. 216
Solve. Assume that y varies inversely as x.
9. If y 5 24 when x 5 2, find y when
x 5 26. 4
10. If y 5 16 when x 5 4, find y when
x 5 6. 32
3
3
11. If y 5 25 when x 5 12.5, find x when
–
y 5 15. 24.16
12. If y 5 7 when x 5 4, find y when
x 5 12. 7
13. If y 5 27 when x 5 12, find x when
y 5 212. 227
14. If y 5 6 when x 5 24, find x when
12
y 5 5 . 210
15. If y 5 60 when x 5 80, find x when
y 5 220. 2240
16. If y 5 40 when x 5 16, find y when
x 5 10. 64
© Glencoe/McGraw-Hill
T33
3
Algebra 1