e x p l o r at i o n
Georgia Performance
Standards
3A
Ordered Pairs
M8A1.b, M8A1.d
At the GasCo station, gasoline costs $3 per gallon. Let x represent
the number of gallons of gasoline that you buy and let y
represent the total cost of the gasoline.
1. Complete the table.
Number of
Gallons, x
1
2
3
4
5
6
Total cost, y
$3
2. Each row of the table contains an ordered pair. An ordered
pair lists an x-value and its corresponding y-value. For
example, the first row of the table contains the ordered pair
(1, 3). Write the ordered pairs in the other rows of your table.
3. The equation y 3x gives the cost of x gallons of gasoline.
Use the equation to find the cost of 12 gallons of gasoline.
4. Write the ordered pair from Problem 3.
Think and Discuss
5. Describe how you could find a new ordered pair for the
above situation.
6. Explain whether you think the ordered pair (1, 3) is the same
as (3, 1).
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70
Holt Mathematics
Name
Date
LAB
Technology Lab
3A
Create a Table of Solutions
Class
The Table feature on a graphing calculator can help you make a
table of values quickly.
Activity
Make a table of solutions of the equation y 2x 3.
Then find the value of y when x 29.
To enter the equation, press the
press 2
X,T,␪,n
Y
. Then
3.
TBLSET
Press 2nd
to go to the Table Setup menu.
In this menu, TblStart shows the starting x-value, and Tbl
shows how the x-values increase. If you need to change
these values, use the arrow keys to highlight the number
you want to change and then type a new number.
WINDOW
TABLE
Press
2nd
GRAPH
to see the table of values.
On this screen, you can see that y 7 when x 5.
Use the arrow keys to scroll down the list. You can see that
y 55 when x 29.
To check, substitute 29 into y 2x 3.
y 2x 3
2(29) 3 58 3 55
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71
Holt Mathematics
Name
Date
LAB
Technology Lab
3A
Create a Table of Solutions, continued
Class
Think and Discuss
1. On an Internet site, pencils can be purchased for 17¢ each, but
they only come in boxes of 12. You decide to make a table to
compare x, the number of pencils, to y, the total cost of the
pencils. What TblStart and Tbl values will you use? Explain.
Try This
For each equation, use a table to find the y-values for the given x-values. Give
the TblStart and Tbl values you used.
1. y 3x 6 for x 1, 3, and 7
x
2. y 4 for x 5, 10, 15, and 20
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72
Holt Mathematics
Name
LESSON
3A
Date
Class
Review for Mastery
Ordered Pairs
(0, 5)
An ordered pair can be used to write a solution for a
two-variable equation. For the equation y x 5, a
solution is (0, 5). When the x-value is 0, the y-value is 5.
x-value
y-value
Which of the ordered pairs (5, 3) or (3, 5) is a solution of y 2x 1?
y 2x 1
3 2(5) 1 Substitute 5 for x
and 3 for y.
3 10 1
39
So, (5, 3) is not a solution
of y 2x 1.
y 2x 1
5 2(3) 1
Substitute 3 for x
and 5 for y.
561
55
So, (3, 5) is a solution
of y 2x 1.
Determine whether each ordered pair is a solution of the given
equation. Write is or is not.
1. y 4x 3; (1, 6)
2. y 4x 3; (0, 3)
3. y x 3; (3, 0)
4. y 5x ; (3, 15)
5. y 3x 4; (5, 3)
6. y 6 x ; (4, 2)
A two-variable equation has infinitely many
solutions. Use a table to find and record
some solutions to a given equation.
Use x 1, 2, and 3, for example, to make
a table of values for y 5x 1. Substitute
each given value of x in the expression for x.
Evaluate the expression to find the value
of y that completes the ordered pair.
x
5x 9 y
(x, y)
1
5(1) 1 4
(1, 4)
2
5(2) 1 9
(2, 9)
3
5(3) 1 14
(3, 14)
Complete each table.
7. y 4x
x
8. y 5x 3
4x y
(x, y)
x
5x 3 y
(x, y)
0
4(0) (0,
)
1
5( ) 3 (1,
)
1
4( ) (1,
)
2
5( ) 3 (2,
)
2
4( ) (2,
)
3
5( ) 3 (3,
)
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73
Holt Mathematics
Name
Date
Class
Homework and Practice
LESSON
3A
Ordered Pairs
Determine whether each ordered pair is a solution
of y 5 3x.
1. (1, 8)
2. (3, 7)
3. (2, 10)
4. (0, 5)
Determine whether each ordered pair is a solution
of y 4x 1.
5. (0, 1)
6. (1, 3)
7. (3, 11)
8. (5, 19)
Use the given values to complete the table of solutions.
9. y x 4 for x 0, 1, 2, 3, 4
x
x4
y
10. y 2x 3 for x 0, 1, 3, 5, 7
(x, y)
x
0
0
1
1
2
3
3
5
4
7
11. y 4x 1 for x 1, 2, 4, 5, 8
x
4x 1
y
2x 3
y
(x, y)
12. y 5x 2 for x 0, 2, 4, 6, 8
(x, y)
x
1
0
2
2
4
4
5
6
8
8
5x 2
y
(x, y)
13. Mrs. Frank had 150 customers when she began her delivery
route. Each month she adds 5 new customers. The equation
that gives the total number of customers, t, in her route is
t 150 5m, where m is the number of months since she
began the route. How many customers will Mrs. Frank have
after 12 months?
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74
Holt Mathematics
Answer Key
Chapter 3 Project Recording Sheet
Review for Mastery 3A
1–2. Check students’ work.
1. is not
3. find 37.5 on the horizontal axis, follow a
vertical line up to the graph, and then
find the corresponding y-value on the
vertical axis (about 200 mg).
2. is
4. Check students’ work.
5. is not
5. Both graphs are straight lines. The graph
of ibuprofen doses is flatter than the
graph of paracetamol doses.
6. is
3. is not
4. is
7.
Exploration 3A
1.
Number of
Gallons, x
Total Cost, y
1
$3
2
$6
3
$9
4
$12
5
$15
6
$18
x
4x y
(x, y)
0
4(0) 0
(0, 0)
1
4(1) 4
(1, 4)
2
4(2) 8
(2, 8)
8.
x
5x 3 y
(x, y)
1
5(1) 3 2
(1, 2)
2
5(2) 3 7
(2, 7)
3
5(3) 3 12
(3, 12)
Homework and Practice 3A
2. (2, 6), (3, 9), (4, 12), (5, 15), (6, 18)
1. yes
3. $36
2. no
4. (12, 36)
3. no
5. Choose a positive integer x-value, and
multiply by 3 for the y-value.
4. yes
6. No, because the order matters.
6. yes
5. no
7. yes
Technology Lab 3A
Think and Discuss
8. yes
9.
1. Tblstart 1, ΔTbl 0.17
Try This
1. 9, 15, 27; Tblstart 1, ΔTbl 1
2. 1.25, 2.5, 3.75, 5; Tblstart 5, ΔTbl 5
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12
x
x4
y
(x, y)
0
4
4
(0, 4)
1
5
5
(1, 5)
2
6
6
(2, 6)
3
7
7
(3, 7)
4
8
8
(4, 8)
Holt Mathematics
Answer Key
Review for Mastery 3B
10.
x
2x 3
y
(x, y)
1. (0, 6)
0
3
3
(0, 3)
2. (–5, 4)
1
5
5
(1, 5)
3. (–2, –6)
3
9
9
(3, 9)
5
13
13
(5, 13)
7
17
17
(7, 17)
4–9.
y
N
8
4
11.
x
4x 1
y
(x, y)
1
3
3
(1, 3)
2
7
7
(2, 7)
4
15
15
(4, 15)
5
19
19
(5, 19)
8
31
31
(8, 31)
K
8
J
O
4
4
8
P
4
M
x
8
10.
12.
x
4x y
(x, y)
0
4(0) 0
(0, 0)
x
x4
y
(x, y)
1
4(1) 4
(1, 4)
0
4
4
(0, 4)
2
4(2) 8
(2, 8)
1
5
5
(1, 5)
2
6
6
(2, 6)
3
7
7
(3, 7)
4
8
8
(4, 8)
y
8
4
x
8
13. 210 customers
O
4
y 4x
4
8
4
Exploration 3B
8
1. left 4, up 6
2. left 6, down 6
Homework and Practice 3B
3. right 7, up 5
4. left 7
1. (4, 0)
5. right 3, down 7
2. (3, –4)
6. First, put the x-coordinate for moving left
(negative number) or right (positive
number). Then write the y-coordinate for
moving down (negative number) or up
(positive number).
3. (–2, 1)
4. (–1, –5)
5. (2, –6)
6. (0, 6)
7. (–4, 5)
8. (7, 5)
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13
Holt Mathematics