Download Review for Mastery 2-7

Name
Date
Class
California Standards Preparation for AF1.0
LESSON
Review for Mastery
2-7
Equations in Two Variables
In the table below, the x-values are the input and the y-values are
the output.
x 0
1
2
3 4
5
6 7
y 4
5
6
7 8
9 10 ?
To write an equation in two variables for a table of
values, first compare the x- and y-values to find a
pattern.
Each y-value is 4 more than its corresponding
x-value.
Then use the pattern to write a rule for the table.
yx4
You can use the rule to find a missing value in a table.
To find the value of y in table above when x 7, substitute
7 for x in the equation.
yx4
y74
y 11
So y is 11 when x is 7.
Write an equation in two variables that gives the values in each
table. Use the equation to find the value of y for the indicated
value of x.
1.
x 1
2
3
4 5
y 3
6
9 12 15 ?
2.
6
x 18 17 16 15 14 13
y 15 14 13 ? 11 10
You can also write equations for relationships that are described in words.
The length of the pool is 6 times the width of the pool.
length of pool
w width of pool
6w
Choose variables for the equation.
Write an equation.
Write an equation for the relationship. Tell what each variable
you use represents.
3. Todd is 6 inches taller than Scott.
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4. Alana is 4 times as old as Tracey.
18
Holt Mathematics
California Standards Preparation for AF1.0
California Standards Preparation for AF1.0
LESSON
Review for Mastery
LESSON
Review for Mastery
2-6
The Coordinate Plane
2-7
Equations in Two Variables
y
The coordinate plane is divided into four
quadrants. They are numbered I, II, III, and IV.
4
II
An ordered pair tells the location of a point. The
x-coordinate tells you how far to move right or
left. The y-coordinate tells you how far to move
up or down.
In the table below, the x-values are the input and the y-values are
the output.
I
2
x
4
2
O
2
x 0
1
2
3 4
5
y 4
5
6
7 8
9 10 ?
6 7
Each y-value is 4 more than its corresponding
x-value.
4
IV
2 x-coordinate
The coordinates of point A are (5, 4) because
it is 5 units to the right of the origin and 4 units
down. It is located in quadrant IV.
IIl
A
Then use the pattern to write a rule for the table.
yx4
y-coordinate
T
4
2. Q
3. F
2
III; (3, 6)
II; (4, 1)
4. T
x-axis; (6, 0)
5. P
x
D
4
2
4
F
4
Write an equation in two variables that gives the values in each
table. Use the equation to find the value of y for the indicated
value of x.
1.
2
6. W
IV; (4, 5)
O
2
I; (5, 5)
W
x 1
2
3
y 3
6
9 12 15 ?
4 5
2.
6
x 18 17 16 15 14 13
y 15 14 13 ? 11 10
P
Q
y-axis; (0, 4)
yx4
y74
y 11
So y is 11 when x is 7.
You can use the rule to find a missing value in a table.
To find the value of y in table above when x 7, substitute
7 for x in the equation.
y
Name the quadrant on axis where each point is
located. Then give the coordinates of each point.
1. D
(5, 4)
4
To write an equation in two variables for a table of
values, first compare the x- and y-values to find a
pattern.
y 3x, y 18
y x 3, y 12
You can also write equations for relationships that are described in words.
The length of the pool is 6 times the width of the pool.
y
Graph each point on the coordinate plane.
7. B (1, 6)
B
2
9. V (3, 4)
10. Z (0, 6)
4
2
O
2
4
6
3. Todd is 6 inches taller than Scott.
2
V
4
6
R
Z
17
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Holt Mathematics
a Alana’s age
s Scott’s height
t Tracey’s age
ts6
a 4t
18
California Standards Preparation for
NS2.3, AF1.0
4. Alana is 4 times as old as Tracey.
t Todd’s height
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All rights reserved.
Holt Mathematics
NS2.4
LESSON
Review for Mastery
LESSON
Review for Mastery
2-8
Graphing Equations
3-1
Prime Factorization
To write the prime factorization of a number, write the number as
the product of only prime numbers. A prime number has only two
factors, itself and 1.
You can express solutions to equations as ordered pairs.
To express solutions to y x 3 as ordered pairs, substitute the given
values for x in the equation. Then write the solutions as ordered pairs.
x
x3
y
ordered pair (x, y)
9
93
6
(9, 6)
7
73
4
(7, 4)
5
53
2
(5, 2)
3
33
0
(3, 0)
18
6
2
x
2x
y
ordered pair (x, y)
1
2•1
2•2
2•3
2•4
2
4
6
8
(1, 2)
(2, 4)
(3, 6)
(4, 8)
2
3
4
9
2
3
3
The prime factorization of 36 is
2 • 2 • 3 • 3, or 22 • 32.
The prime factorization of 18 is
2 • 3 • 3, or 2 • 32.
2. 28
22 • 5
y
(9, 6)
(7, 4)
4
(5, 2)
(3, 0)
4
y=x3
3. 54
22 • 7
4. 63
2 • 33
32 • 7
O
4
2|60
2|30
3|15
5|5
1
8
4
4
8
4
y = 2x
O
1) The divisors must be prime numbers.
2) Keep dividing until the quotient is 1.
3) The divisors are the factors in the
prime factorization.
The prime factorization of 60 is
2 • 2 • 3 • 5, or 22 • 3 • 5.
y
8
Use a step diagram to find the prime
factorization of 75.
Use a step diagram to find the prime
factorization of 60.
x
8
(4, 8)
(3, 6)
(2, 4)
(1, 2)
4
3|75
5|25
5|5
1
The prime factorization of 75 is
3 • 5 • 5, or 3 • 52.
Use a step diagram to find the prime factorization.
x
5. 48
8
6. 24
7. 40
8. 98
4
8
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2
8
8
19
4
3
1. 20
2. Graph the function described by y 2x.
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36
Keep factoring until all
the factors are prime.
3
Use a factor tree to find the prime factorization.
You can graph solutions of an equation on
a coordinate plane. If the graph of the
solution is a straight line, then the equation
is a linear equation.
Use ordered pairs to graph functions.
The first number, the x-coordinate, tells
you how far to move right or left from
the origin. The second coordinate, the
y-coordinate, tells you how far to
move up or down.
Use a factor tree to find the prime
factorization of 36.
Use a factor tree to find the prime
factorization of 18.
Use the given x-values to write solutions to y 2x as ordered pairs.
1.
Write an equation.
Write an equation for the relationship. Tell what each variable
you use represents.
x
6
Choose variables for the equation.
ᐉ 6w
4
8. R (8, 5)
California Standards
ᐉ length of pool
w width of pool
6
24 • 3
Holt Mathematics
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All rights reserved.
5
23 • 3
23 • 5
20
2 • 72
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