1. Chapter 12
Algebra and Graphing
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2. Algebra and Graphing
12
Lesson 12-1 Negative Numbers
Lesson 12-2 Find Points on a Grid
Lesson 12-3 Graph Ordered Pairs
Lesson 12-4 Problem-Solving Strategy: Use
Logical Reasoning
Lesson 12-5 Functions
Lesson 12-6 Graph Functions
Lesson 12-7 Problem-Solving Investigation:
Choose a Strategy

3. 12-1 Negative Numbers
Five-Minute Check (over Chapter 11)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3

4. 12-1 Negative Numbers
• I will understand and use negative numbers.
• positive number
• negative number

5. 12-1 Negative Numbers
Standard 4NS1.8 Use concepts of
negative numbers (e.g., on a number line, in
counting, in temperature, and in “owing”).

6. 12-1 Negative Numbers
Write the number that represents the situation.
Then show the number on a number line. Sara
owes her mom $5.
When you owe money, it is a decrease.
The number is –5.

7. 12-1 Negative Numbers
Write the number that represents the situation.
The temperature is 7 below zero.
A. –7
B. 7
C. 0
D. –8

8. 12-1 Negative Numbers
Write the number that represents the situation.
Then show the number on a number line. Grant
earned $7 for shoveling Mr. Lincoln’s driveway.
When you earn money, it is an increase.
The number is 7 or +7.

9. 12-1 Negative Numbers
Write the number that represents the situation.
Julia deposits $25 into her bank account.
A. 0
B. 25
C. –25
D. 30

10. 12-1 Negative Numbers
Write the number of each letter on the number line.
A is between –4 and –2. So, A is –3.
B is between –2 and 0. So, B is –1.
C is the same distance from zero as +4.
Answer: So, C is +4.

11. 12-1 Negative Numbers
Write the number of each letter on the number line.
A. –5; –4; –3
B. –3; –1; 4
C. –3; –2; –1
D. –3; 1; 4

13. 12-2 Find Points on a Grid
Five-Minute Check (over Lesson 12-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2

14. 12-2 Find Points on a Grid
• I will use ordered pairs to find and name points on
a grid.
• coordinate plane • y-axis
• origin • ordered pair
• x-axis • coordinates

15. 12-2 Find Points on a Grid
Preparation for Standard 4MG2.1 Draw the
points corresponding to linear relationships on
graph paper (e.g., draw 10 points on the graph of
the equation y = 3x and connect them by using a
straight line).

16. 12-2 Find Points on a Grid
What is
located at
point (2, 5)?
To find (2, 5), start at
(0, 0). Move right 2
units. Then, move up
5 units.
Answer: The ordered pair (2, 5) locates the post office.

17. 12-2 Find Points on a Grid
What is located at
point (1, 3)?
A. red house
B. blue house
C. tan house

18. 12-2 Find Points on a Grid
What letter is located
at (–3, 5)?
To find (–3, 5), start at
(0, 0). The –3 tells you
to move 3 units to the
left. The 5 tells you to
move 5 units up.
Answer: The ordered pair (–3, 5) locates the letter C.

19. 12-2 Find Points on a Grid
What letter is located
at (–4, 2)?
A. Q
B. R
C. S

21. 12-3 Graph Ordered Pairs
Five-Minute Check (over Lesson 12-2)
Main Idea and Vocabulary
California Standards
Key Concept: Length of Line Segments
Example 1
Example 2

22. 12-3 Graph Ordered Pairs
• I will graph ordered pairs and find the lengths
of line segments on a coordinate grid.
• graph

23. 12-3 Graph Ordered Pairs
Standard 4MG2.2 Understand that the
length of a horizontal line segment equals
the difference of the x-coordinates.
Standard 4MG2.3 Understand that the
length of a vertical line segment equals the
difference of the y-coordinates.

24. 12-3 Graph Ordered Pairs

25. 12-3 Graph Ordered Pairs
P
Graph point P at (–2, 4).
Step 1 Start at (0, 0).
Step 2 The x-coordinate
is –2. So, move 2
units to the left.
Step 3 The y-coordinate
is 4. So, move 4
units up.
Step 4 Graph a point at (–2, 4). Label it P.

26. 12-3 Graph Ordered Pairs
Choose which graph shows point A at (1, 4).
A. B.

27. 12-3 Graph Ordered Pairs
Choose which graph shows point A at (1, 4).
C. D.

28. 12-3 Graph Ordered Pairs
Choose which graph shows point A at (1, 4).
C.

29. 12-3 Graph Ordered Pairs
Find the distance
between (2, 2) and
(2, 6).
The line segment is
vertical. Subtract the y-
coordinates.
length of segment
=6–2
=4
Answer: The length is 4 units.

30. 12-3 Graph Ordered Pairs
Find the distance between (1, 5) and (1, 2).
A. 2 units
B. 3 units
C. 4 units
D. 5 units

32. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Five-Minute Check (over Lesson 12-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy

33. 12-4 Problem-Solving Strategy: Use Logical Reasoning
• I will solve problems using logical reasoning.

34. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information,
and observing patterns.

35. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Standard 4SDAP1.1 Formulate survey questions;
systematically collect and represent data on a
number line; and coordinate graphs, tables, and
charts.

36. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Bella, Devan, Carl, and Jill live on Ash, Pine, Maple,
and Oak Streets. Bella lives on Ash. Devan does
not live on Pine. Carl lives on Maple. What street
does Jill live on?

37. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Understand
What facts do you know?
• The four students live on Ash, Pine,
Maple, and Oak Streets.
• Bella lives on Ash Street.
• Devan does not live on Pine Street.
• Carl lives on Maple Street.
What do you need to find?
• Find what street Jill lives on.

38. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Plan
You can use logical reasoning and a table to solve
the problem.

39. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Solve
• Bella lives on Ash and Carl lives on Maple. So Jill
cannot live on either of these streets.
• Devan does not live on Pine Street. He must live
on Oak Street.
Answer: So, Jill must live on Pine Street.

40. 12-4 Problem-Solving Strategy: Use Logical Reasoning
Check
Look back at the problem. The answer makes sense
for the facts given in the problem.
So, the answer is correct.

42. 12-5 Functions
Five-Minute Check (over Lesson 12-4)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3

43. 12-5 Functions
• I will complete function tables.
• function

44. 12-5 Functions
Standard 4AF1.5 Understand that an
equation, such as y = 3x + 5, is a prescription
for determining a second number when a first
number is given.

45. 12-5 Functions
Jake makes a $2 profit for each magazine
subscription he sells. Complete the function
table to show the profits earned for the number
of subscriptions sold.
Make a table to find how
much money Jake will
make for the number of
subscriptions sold. 4 2 8
Multiply each input by 2 6 2 12
to find each output.

46. 12-5 Functions
Anita makes $5 for every yard she rakes leaves for.
Complete the function table to show the profits
earned for the number of yards raked.
A. 4 × 2 = 8; 6 × 2 = 12
B. 5 × 4 = 25; 5 × 6 = 35
C. 5 × 4 = 20; 5 × 6 = 30
D. 4 × 4 = 16; 6 × 6 = 36

47. 12-5 Functions
Use the rule y = 4x to complete a function table
where the input is 4, 6, 8, 10.
The rule y = 4x
means to multiply x
by 4 to get y.

48. 12-5 Functions
Use the rule y = 5x to complete a function table
where the input is 2, 4, 6, 8. What is the output for
each input?
A. 10, 20, 30, 40
B. 5, 10, 15, 20
C. 7, 9, 11, 13
D. 2, 4, 6, 8

49. 12-5 Functions
Use the rule y = 2x + 5 to complete a function table
where the input is 3, 5, 7.
First, multiply x by 2.
Then, add 5 to the
product to get y.

50. 12-5 Functions
Use the rule y = 4x + 1 to complete a function table
where the input is 2, 4, 6. What is the output for
each input?
A. 8, 16, 24
B. 9, 17, 25
C. 2, 4, 6
D. 3, 5, 7

52. 12-6 Graph Functions
Five-Minute Check (over Lesson 12-5)
Main Idea
California Standards
Example 1
Example 2
Graph Functions

53. 12-6 Graph Functions
• I will graph functions.

54. 12-6 Graph Functions
Standard 4MG2.1 Draw the points
corresponding to linear relationships on graph
paper (e.g., draw 10 points on the graph of the
equation y = 3x and connect them by using a
straight line).

55. 12-6 Graph Functions
Each smoothie at the bakery costs $3. The function
table shows how much it will cost if you buy
1, 2, 3, or 4 smoothies. Write the ordered pairs and
graph the function y = 3x. Then use the graph to
find how much 6 smoothies will cost.
Step 1 Write the
ordered pairs.
Then graph.

56. 12-6 Graph Functions
Step 2 Extend the
pattern in the
graph by drawing
a straight line.
The straight line
will help you see
the pattern.
Answer: So, 6 smoothies
will cost $18.

57. 12-6 Graph Functions
Noah gets $11 a week for allowance. Find ordered
pairs and graph y = 11x to find how much money
Noah will have after 8 weeks.
A. $70
B. $75
C. $80
D. $88

58. 12-6 Graph Functions
Graph 10 points on the graph of the function
y = 3x – 1.
Complete a table to
find the ordered pairs.

59. 12-6 Graph Functions
Then graph the ordered
pairs on a coordinate
plane. Connect the
points with a straight line.

60. 12-6 Graph Functions
Choose the correct chart of ordered pairs and graph
that go with the equation y = 2x + 2.
A.

61. 12-6 Graph Functions
Choose the correct chart of ordered pairs and graph
that go with the equation y = 2x + 2.
B.

62. 12-6 Graph Functions
Choose the correct chart of ordered pairs and graph
that go with the equation y = 2x + 2.
C.

63. 12-6 Graph Functions
Choose the correct chart of ordered pairs and graph
that go with the equation y = 2x + 2.
D.

64. 12-6 Graph Functions
Choose the correct chart of ordered pairs and graph
that go with the equation y = 2x + 2.
D.

66. 12-7 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 12-6)
Main Idea
California Standards
Example 1: Problem-Solving Investigation

67. 12-7 Problem-Solving Investigation: Choose a Strategy
• I will solve problems by choosing the best
strategy.

68. 12-7 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant
information, sequencing and prioritizing
information, and observing patterns.

69. 12-7 Problem-Solving Investigation: Choose a Strategy
Standard 4AF1.5 Understand that an
equation such as y = 3x + 5 is a prescription
for determining a second number when a
first number is given.

70. 12-7 Problem-Solving Investigation: Choose a Strategy
AIDEN: I just got a new video game
system. Games cost $20. Felice has
the older version of the video game
system. Her games cost $15. How
many video games can we each buy if
we each have $60?
YOUR MISSION: Find out how many
games each person can buy.

71. 12-7 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Games for Aiden’s game system cost $20.
• Games for Felice’s game system cost $15.
• Each has $60 to spend on video games.
What do you need to find?
• Find how many games each person can buy.

72. 12-7 Problem-Solving Investigation: Choose a Strategy
Plan
To find the answer, organize the data to show the
number of games and the total amount of money
spent.

73. 12-7 Problem-Solving Investigation: Choose a Strategy
Solve
Answer: Since Aiden’s games cost more, he can
only buy 3, whereas Felice can buy 4.

74. 12-7 Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Since 20 × 3 = 60 and
15 × 4 = 60, you know that the answer is correct.

76. Algebra and Graphing
12
Five-Minute Checks
Graph Functions

77. Algebra and Graphing
12
Lesson 12-1 (over Chapter 11)
Lesson 12-2 (over Lesson 12-1)
Lesson 12-3 (over Lesson 12-2)
Lesson 12-4 (over Lesson 12-3)
Lesson 12-5 (over Lesson 12-4)
Lesson 12-6 (over Lesson 12-5)
Lesson 12-7 (over Lesson 12-6)

78. Algebra and Graphing
12
(over Chapter 11)
Find the area of the figure.
4
A. 60 6
6
B. 36 4
C. 56
D. 48

79. Algebra and Graphing
12
(over Lesson 12-1)
Write the number of letter A on the number line.
A. –2
B. 3
C. –3
D. –1

80. Algebra and Graphing
12
(over Lesson 12-1)
Write the number of letter B on the number line.
A. 3
B. 1
C. –2
D. 2

81. Algebra and Graphing
12
(over Lesson 12-1)
Write the number of letter C on the number line.
A. –4
B. 4
C. 2
D. 3

82. Algebra and Graphing
12
(over Lesson 12-2)
Write the ordered pair that names point A.
A. (2, –2)
B. (–1, 2)
C. (–2, 2)
D. (–2, –2)

83. Algebra and Graphing
12
(over Lesson 12-2)
Write the ordered pair that names point B.
A. (–5, –1)
B. (5, 1)
C. (–5, 2)
D. (–5, 1)

84. Algebra and Graphing
12
(over Lesson 12-2)
Write the ordered pair that names point C.
A. (–4, 3)
B. (4, –3)
C. (–4, –3)
D. (4, 3)

85. Algebra and Graphing
12
(over Lesson 12-3)
Find the length of the horizontal or vertical line
segment formed by the following set of ordered
pairs: (5, 4), (1, 4).
A. 6
B. 9
C. 4
D. 5

86. Algebra and Graphing
12
(over Lesson 12-3)
Find the length of the horizontal or vertical line
segment formed by the following set of ordered
pairs: (–3, 6), (–3, 0).
A. 3
B. 6
C. 9
D. 0

87. Algebra and Graphing
12
(over Lesson 12-4)
Hugo has horses and ducks on his farm. He has 3
times as many horses as he does ducks. Together,
the animals have 14 legs. How many horses and
ducks does Hugo have?
A. 1 horse, 3 ducks
B. 2 horses, 3 ducks
C. 1 horse, 5 ducks
D. 3 horses, 1 duck

88. Algebra and Graphing
12
(over Lesson 12-5)
Use the rule to complete the function table.
A. 5, 6, 7
B. 9, 18, 27
C. 6, 9, 12
D. 5, 8, 11

89. Algebra and Graphing
12
(over Lesson 12-6)
Choose the set of points that belong on the graph of
the function y = 2x.
A. (1, 2), (3, 6), (5, 8)
B. (1, 3), (2, 4), (3, 5)
C. (2, 1), (4, 2), (6, 3)
D. (1, 2), (2, 4), (3, 6)

90. Algebra and Graphing
12
(over Lesson 12-6)
Choose the set of points that belong on the graph of
the function 2x = y.
A. (20, 10), (18, 9), (16, 8)
B. (10, 12), (9, 11), (8, 10)
C. (10, 20), (9, 18), (8, 16)
D. (10, 20), (18, 9), (8, 16)

91. This slide is intentionally blank.