Download Graph each ordered pair on a coordinate plane. 2. A(2, 5

1-6 Ordered Pairs and Relations
Graph each ordered pair on a coordinate plane.
2. A(2, 5)
SOLUTION: Start at the origin. The x-coordinate is 2, so move 2 units to the right. The y-coordinate is 5, so move 5 units up.
Draw a dot, and label it A.
4. Z(0, 1)
SOLUTION: Start at the origin. The x-coordinate is 0, so you do not need to move to the right. The y-coordinate is 1, so move 1
unit up. Draw a dot, and label it Z.
Refer to the coordinate plane shown below. Write the ordered pair that names each point.
6. K
SOLUTION: Start at the origin. Move right on the x-axis to find the x-coordinate of point K, which is 2. Move up the y-axis to find
the y-coordinate, which is 1.
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The ordered pair for point K is (2, 1).
1-6 Ordered Pairs and Relations
Refer to the coordinate plane shown below. Write the ordered pair that names each point.
6. K
SOLUTION: Start at the origin. Move right on the x-axis to find the x-coordinate of point K, which is 2. Move up the y-axis to find
the y-coordinate, which is 1.
The ordered pair for point K is (2, 1).
8. M
SOLUTION: Start at the origin. Move right on the x-axis to find the x-coordinate of point M , which is 6. Move up the y-axis to find
the y-coordinate, which is 6.
The ordered pair for point M is (6, 6).
Express each relation as a table. Then determine the domain and range.
10. {(1, 3), (2, 6), (3, 3), (4, 7)}
SOLUTION: x
y
1
3
2
6
3
3
4
7
The domain is {1, 2, 3, 4} and the range is {3, 6, 7}.
Graph each ordered pair on a coordinate plane.
12. A(4, 7)
SOLUTION: Start at the origin. The x-coordinate is 4, so move 4 units to the right. The y-coordinate is 7, so move 7 units up.
Draw a dot, and label it A.
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14. C(7, 3)
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2
6
3
3
4
7
1-6 Ordered
Pairs
and
The domain
is {1,
2, Relations
3, 4} and the range is {3, 6, 7}.
Graph each ordered pair on a coordinate plane.
12. A(4, 7)
SOLUTION: Start at the origin. The x-coordinate is 4, so move 4 units to the right. The y-coordinate is 7, so move 7 units up.
Draw a dot, and label it A.
14. C(7, 3)
SOLUTION: Start at the origin. The x-coordinate is 7, so move 7 units to the right. The y-coordinate is 3, so move 3 units up.
Draw a dot, and label it C.
16. F(6, 1)
SOLUTION: Start at the origin. The x-coordinate is 6, so move 6 units to the right. The y-coordinate is 1, so move 1 unit up. Draw
a dot, and label it F.
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1-6 Ordered Pairs and Relations
16. F(6, 1)
SOLUTION: Start at the origin. The x-coordinate is 6, so move 6 units to the right. The y-coordinate is 1, so move 1 unit up. Draw
a dot, and label it F.
18. H(3, 0)
SOLUTION: Start at the origin. The x-coordinate is 3, so move 3 units to the right. The y-coordinate is 0, so you do not need to
move up. Draw a dot, and label it H.
Refer to the coordinate system shown below. Write the ordered pair that names each point.
20. L
SOLUTION: The x-coordinate of point L is 2, and the y-coordinate is 4. The ordered pair for point L is (2, 4).
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SOLUTION: Page 4
20. L
SOLUTION: 1-6 Ordered Pairs and Relations
The x-coordinate of point L is 2, and the y-coordinate is 4. The ordered pair for point L is (2, 4).
22. N
SOLUTION: The x-coordinate of point N is 2, and the y-coordinate is 1. The ordered pair for point N is (2, 1).
24. Q
SOLUTION: The x-coordinate of point Q is 3, and the y-coordinate is 7. The ordered pair for point Q is (3, 7).
26. S
SOLUTION: The x-coordinate of point S is 5, and the y-coordinate is 0. The ordered pair for point S is (5, 0).
Express each relation as a table. Then determine the domain and range.
28. {(4, 5), (2, 1), (5, 0), (3, 2)}
SOLUTION: x
4
2
5
3
y
5
1
0
2
The domain is {2, 3, 4, 5} and the range is {0, 1, 2, 5}.
30. {(6, 0), (4, 5), (2, 1), (3, 1)}
SOLUTION: x
y
6
0
4
5
2
1
3
1
The domain is {2, 3, 4, 6} and the range is {0, 1, 5}.
32. The cost of a mini pizza is $7 at Pizza Pizza.
a. Make a table of ordered pairs in which the x-coordinate represents the number of mini pizzas and the y-coordinate
represents the cost of 1, 3, 5, and 7 mini pizzas at Pizza Pizza.
b. Graph the ordered pairs. Then describe the graph.
SOLUTION: a. 1 pizza costs $7
(x, y)
x (Number
y (Cost, $)
of Pizzas)
1
(1, 7)
7 × 1 = 7
3
(3, 21)
7 × 3 = 21
5
(5, 35)
7 × 5 = 35
7
(7, 49)
7 × 7 = 49
b.
The number of pizzas is graphed along the x-axis. The cost is graphed along the y-axis.
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6
0
4
5
2
1
3 Pairs and
1 Relations
1-6 Ordered
The domain is {2, 3, 4, 6} and the range is {0, 1, 5}.
32. The cost of a mini pizza is $7 at Pizza Pizza.
a. Make a table of ordered pairs in which the x-coordinate represents the number of mini pizzas and the y-coordinate
represents the cost of 1, 3, 5, and 7 mini pizzas at Pizza Pizza.
b. Graph the ordered pairs. Then describe the graph.
SOLUTION: a. 1 pizza costs $7
(x, y)
x (Number
y (Cost, $)
of Pizzas)
1
(1, 7)
7 × 1 = 7
3
(3, 21)
7 × 3 = 21
5
(5, 35)
7 × 5 = 35
7
(7, 49)
7 × 7 = 49
b.
The number of pizzas is graphed along the x-axis. The cost is graphed along the y-axis.
The points appear to lie in a line that slants up from left to right.
34. Multiple Representations In this problem, you will explore more about relations. Suppose Jamal has only 30
minutes to practice the piano and study for a science test.
a. Table Make a table of ordered pairs showing at least 6 ways Jamal can split the time between the two activities.
Let the x-coordinate represent the number of minutes spent playing the piano and the y-coordinate represent the
number of minutes spent studying, respectively.
b. Graph Graph the ordered pairs.
c. Words Describe the general pattern of points of your graph.
d. Graph Choose a point on the graph that is not one of the points you plotted. Use the coordinates to predict a pair
of values for the piano time and study time.
SOLUTION: a. Find six pairs of numbers that have a sum of 30.
x
y
(x, y)
(Piano Time,
(Study Time,
min)
min)
5
30 – 5 = 25
(5, 25)
10
30 – 10 = 20
(10, 20)
15
30 – 15 = 15
(15, 15)
20
30 – 20 = 10
(20, 10)
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25
30 – 25 = 5
(25, 5)
30
30 – 30 = 0
(30, 0)
b. Jamal’s piano time is graphed along the x-axis. His study time is graphed along the y-axis.
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x
y
(x, y)
(Piano Time,
(Study Time,
min)
min)
5
30
5 = 25
(5, 25)
–
1-6 Ordered Pairs and Relations
10
30 – 10 = 20
(10, 20)
15
30 – 15 = 15
(15, 15)
20
30 – 20 = 10
(20, 10)
25
30 – 25 = 5
(25, 5)
30
30 – 30 = 0
(30, 0)
b. Jamal’s piano time is graphed along the x-axis. His study time is graphed along the y-axis.
c. The points appear to lie in a straight line that slants down from left to right.
d.
Sample answer: (12, 18): If Jamal spends12 minutes playing the piano, he will have 18 minutes left to study for the
test.
36. Multiple Representations The numbers 4, 7, 10, 13, … form an arithmetic sequence because each term can be
found by adding the same number to the previous term.
a. Numbers Write the set of ordered pairs (term number, term).
b. Graph Graph the ordered pairs.
c. Words Describe the shape of the graph.
d. Words If possible, write a rule to find the twentieth term. Explain how you found the rule or why you cannot
write a rule.
SOLUTION: a. The set of ordered pairs is {(1, 4), (2, 7), (3, 10), (4, 13)}.
b.
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Sample answer:
(12, 18):
If Jamal spends12 minutes playing the piano, he will have 18 minutes left to study for the
1-6 Ordered
Pairs and
Relations
test.
36. Multiple Representations The numbers 4, 7, 10, 13, … form an arithmetic sequence because each term can be
found by adding the same number to the previous term.
a. Numbers Write the set of ordered pairs (term number, term).
b. Graph Graph the ordered pairs.
c. Words Describe the shape of the graph.
d. Words If possible, write a rule to find the twentieth term. Explain how you found the rule or why you cannot
write a rule.
SOLUTION: a. The set of ordered pairs is {(1, 4), (2, 7), (3, 10), (4, 13)}.
b.
c. The points appear to lie in a straight line that slants up and to the right. The graph shows a positive, linear
relationship.
d.
Term
Number
Term
1
2
3
4
1 × 3 + 1=4
2 × 3 + 1=7
3 × 3 + 1 = 10
4 × 3 + 1 = 13
Multiplying the term number by 3 and adding 1 gives the term. So, you would multiply 3 times the x value plus 1
equals the y-value. The twentieth term would be 20 × 3 + 1 or 61.
38. Persevere with Problems Describe all of the possible locations for the graph of (x, y) if x = 2.
SOLUTION: x = 2 at every point that is 2 units to the right of the y-axis. So, the graph of (x, y) where x = 2 is the vertical line x =
2.
40. Building on the Essential Question Explain why the point M (4, 3) is different from the point N(3, 4).
SOLUTION: Sample answer: Point M is 4 units to the right on the x-axis and 3 units up the y-axis. Point N is 3 units to the right on
the x-axis and 4 units up the y-axis.
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38. Persevere with Problems Describe all of the possible locations for the graph of (x, y) if x = 2.
SOLUTION: x = 2 at every
is 2 units to the right of the y-axis. So, the graph of (x, y) where x = 2 is the vertical line x =
1-6 Ordered
Pairspoint
andthat
Relations
2.
40. Building on the Essential Question Explain why the point M (4, 3) is different from the point N(3, 4).
SOLUTION: Sample answer: Point M is 4 units to the right on the x-axis and 3 units up the y-axis. Point N is 3 units to the right on
the x-axis and 4 units up the y-axis.
42. Rectangle ABCD has vertices A(1, 3), B(1, 6), and C(5, 6). What are the coordinates of point D?
F (6, 5)
G (5, 1)
H (5, 3)
J (6, 1)
SOLUTION: For the points to make a rectangle, the coordinates of point D would be (5, 3). Choice H is correct.
44. Short Response Point Z is located at (4, 7) on a coordinate plane. Point T is located 3 units to the right and 4 units
down from point Z. What is the x-coordinate of point T?
SOLUTION: The x-coordinate of Point Z is 4. If Point T is 3 units to the right of Point Z, then the x-coordinate of Point T is 4 + 3
or 7.
Name the property shown by each statement.
46. 6 • 2 • 0 = 0
SOLUTION: When any number is multiplied by 0, the product is 0. This is the Multiplicative Property of Zero.
48. (5 + x) + 6 = 5 + (x + 6)
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The grouping of the numbers changed. This is the Associative Property of Addition.
State whether each conjecture is true. If not, give a counterexample.
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Name the property shown by each statement.
46. 6 • 2 • 0 = 0
SOLUTION: 1-6 Ordered
and
When anyPairs
number
is Relations
multiplied by 0, the product is 0. This is the Multiplicative Property of Zero.
48. (5 + x) + 6 = 5 + (x + 6)
SOLUTION: The grouping of the numbers changed. This is the Associative Property of Addition.
State whether each conjecture is true. If not, give a counterexample.
50. Subtraction of whole numbers is commutative.
SOLUTION: 9– 3=6
3 – 9 = –6
6 ≠ -6 and therefore 9 – 3 ≠ 3 – 9
No, subtraction of whole numbers is not commutative.
Find the value of each expression.
52. x + 7 if x = 8
SOLUTION: 54. 18 + m if m = 4
SOLUTION: 56. s + 14 if s = 32
SOLUTION: Find the value of each expression.
58. 8 + 12 × 4 ÷ 8
SOLUTION: 60. 14 – 2 × 7 + 0
SOLUTION: 62. 11+ 4 × (12 – 7)
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SOLUTION: 1-6 Ordered Pairs and Relations
62. 11+ 4 × (12 – 7)
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