Download Reading 5.1

Name ________________________________________ Date __________________ Class__________________
LESSON
5-1
Reading Strategy
Compare and Contrast
Variations can be direct variations or inverse variations.
In direct variation, y varies directly as x:
y  kx
The graph of direct variation is a straight line.
In inverse variation, y varies inversely as x:
k
y
x
The graph of inverse variation is undefined
when x  0.
Determine whether each represents direct or inverse variation.
1. The number of pancakes made and the amount of pancake mix used
______________
2. The price of milk and the number of gallons you can buy for $20.00
______________
3. The outside temperature in the winter and the amount of fuel required
to heat a house
______________
4. A child’s age and his height
______________
5. The number of apples purchased and the total cost
______________
Answer each question.
6.
a. Kelly runs for exercise. Explain how the distance she runs varies as her
running speed.
_____________________________________________________________________________________
b. Write an equation showing the relationship between
the distance she runs, d, and her running speed, s.
7.
_______________________
a. Cal made some pizzas for his party. Explain how the number of slices per
person varies as the number of people at the party.
_____________________________________________________________________________________
b. Write an equation showing the relationship between
the number of slices per person, p, and the number of
people at the party, n.
_______________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-10
Holt McDougal Algebra 2
3. $3.00
Problem Solving
4. 15 h
5. 8 bushels
1. a. t =
6. 234 trillionths of a cm
b. k = 975
Reteach
c. It is the total number of student hours
that it takes to build a 7-foot sailboat.
1. a. k = 1.5
b. y = 1.5x
d. 81.25 h
c. y = 1.5x; y = 1.5 ⋅ 50; y = 75
2. 13 students
2. a. y = kxz; 150 = k ⋅ 2.5 ⋅ 12; 150 = 30k,
k=5
b. y = 5xz
b. y =
3. C
4. B
5. D
6. B
Reading Strategies
c. y = 5xz; y = 5 ⋅ 4 ⋅ 6.5; y = 130
3. a. y =
k
s
k
k
; 2 = ; k = 18
x
9
1. Direct
2. Inverse
3. Inverse
4. Direct
18
x
5. Direct
6. a. As her speed increases, the number
of miles she runs increases, so it is
direct variation.
18
18
;y =
;y =3
c. y =
x
6
b. d = ks
7. a. As the number of people at the party
increases, the number of slices per
person decreases, so it is inverse
variation.
b. p =
k
n
5-2 MULTIPLYING AND DIVIDING
RATIONAL EXPRESSIONS
Practice A
Challenge
1. F =
1. Possible answer: If the denominator is
0, then the expression is undefined
because division by 0 is impossible.
Gm1m2
r2
2. About 6.67 × 10−11Nm2per kg2
2. x = 3
kv 2
3. About 4.43 × 10 N 4. H =
r
−7
1
5. Reduce the resistance by a factor of .
3
6. Double the voltage.
k T
7. F =
L
8. It would increase by a factor of
2.
9. The length could be doubled or the
tension cut by a factor of 4.
3.
5
;x≠0
x2
4.
x+3
;x≠0
x2
5.
2
; x ≠ −3
3
6.
2x + 7
; x ≠ −3
x+3
7.
3x
y2
8.
2x 4
3y 2
9.
4
x−2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A55
Holt McDougal Algebra 2