Download Lesson 7-1 - Saint John Vianney Catholic School

1-7
1-7 Ordered
OrderedPairs
Pairs
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
1-7 Ordered Pairs
Warm Up
Solve.
1. x  8 = 19
3. 7 + n = 24
x = 27
a=7
n = 17
4. 3c  7 = 32
c = 13
5. 17y + 7 = 58
y=3
2. 5 = a  2
Pre-Algebra
1-7 Ordered Pairs
Problem of the Day
A moving van travels 50 miles per hour.
Use the equation y = 50x. How far will
the van travel in 4.5 hours?
225 miles
Pre-Algebra
1-7 Ordered Pairs
Learn to write solutions of equations in two
variables as ordered pairs.
Pre-Algebra
1-7 Ordered Pairs
Vocabulary
ordered pair
Pre-Algebra
1-7 Ordered Pairs
A sign at the store reads “Birthday Banners
$8. Personalize for $1 per letter.”
Cecilia has 7 letters in her name, and
Dowen has 5 letters in his. Figure out how
much it will cost to get a personalized
birthday banner for each of them.
Pre-Algebra
1-7 Ordered Pairs
Price of
banner
=
$8
+
$1
•
Number of letters
in name
Let y be the price of the banner and x be the
number of letters in the name; the equation
for the price of a banner is y = 8 + x.
For Cecelia’s banner: x = 7, y = 8 + 7 or y = 15
For Dowen’s banner:
Pre-Algebra
x = 5, y = 8 + 5 or y = 13
1-7 Ordered Pairs
A solution of a two-variable equation is
written as an ordered pair.
When the numbers in the ordered pair are
substituted in the equation, the equation is
true.
(7, 15) is a solution 
15 = 7 + 8
(5, 13) is a solution 
13 = 5 + 8
(x, y) 
Pre-Algebra
Ordered pair
1-7 Ordered Pairs
Additional Example 1A: Determining If an Ordered
Pair Is a Solution of an Equation
Determine whether the ordered pair is a
solution of y = 4x – 1.
A. (3, 11)
y = 4x – 1
?
11 = 4(3) – 1 Substitute 3 for x and 11 for y.
?
11= 11 
A solution since 11=11.
(3, 11) is a solution.
Pre-Algebra
1-7 Ordered Pairs
Additional Example 1B: Determining If an Ordered
Pair Is a Solution of an Equation
Determine whether the ordered pair is a
solution of y = 4x – 1.
B. (10, 3)
y = 4x – 1
?
3 = 4(10) – 1
?
3 = 39 
Substitute 10 for x and 3 for y.
(10, 3) is not a solution.
Pre-Algebra
1-7 Ordered Pairs
Additional Example 1C: Determining If an Ordered
Pair Is a Solution of an Equation
Determine whether the ordered pair is a
solution of y = 4x – 1.
C. (11, 43)
y = 4x – 1
?
43 = 4(11) – 1
?
43 = 43 
Substitute 11 for x and 43 for y.
A solution since 43 = 43.
(11, 43) is a solution.
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 1A
Determine whether the ordered pair is a
solution of y = 5x + 3.
A. (7, 38)
y = 5x + 3
?
38 = 5(7) + 3
?
38 = 38 
Substitute 7 for x and 38 for y.
(7, 38) is a solution.
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 1B
Determine whether the ordered pair is a
solution of y = 5x + 3.
B. (9, 17)
y = 5x + 3
?
17 = 5(9) + 3
?
17 = 48 
Substitute 9 for x and 17 for y.
(9, 17) is not a solution.
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 1C
Determine whether the ordered pair is a
solution of y = 5x + 3.
C. (10, 53)
y = 5x + 3
?
53 = 5(10) + 3
?
53 = 53 
Substitute 10 for x and 53 for y.
(10, 53) is a solution.
Pre-Algebra
1-7 Ordered Pairs
Additional Example 2A: Creating a Table of Ordered
Pair Solutions
Use the given values to make a table of
solutions.
A. y = 7x for x = 1, 2, 3, 4
x
7x
y
(x, y)
1
7(1)
7
(1, 7)
2
7(2)
14
(2, 14)
3
7(3)
21
(3, 21)
4
7(4)
28
(4, 28)
Pre-Algebra
1-7 Ordered Pairs
Additional Example 2B: Creating a Table of Ordered
Pair Solutions
Use the given values to make a table of
solutions.
B. n = 6m – 5 for m = 1, 2, 3, 4
m
1
2
3
4
6m – 5 6(1) – 5 6(2) – 5 6(3) – 5 6(4) – 5
n
1
7
13
19
(m, n)
(1, 1)
(2, 7)
(3, 13)
Pre-Algebra
(4, 19)
1-7 Ordered Pairs
Try This: Example 2A
Use the given values to make a table of
solutions.
A. y = 6x for x = 1, 2, 3, 4
x
6x
y
(x, y)
1
6(1)
6
(1, 6)
2
6(2)
12
(2, 12)
3
6(3)
18
(3, 18)
4
6(4)
24
(4, 24)
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 2B
Use the given values to make a table of
solutions.
B. n = 8m – 2 for m = 1, 2, 3, 4
m
1
2
3
4
8m – 2 8(1) – 2 8(2) – 2 8(3) – 2 8(4) – 2
n
6
14
22
30
(m, n)
(1, 6)
(2, 14)
(3, 22)
Pre-Algebra
(4, 30)
1-7 Ordered Pairs
Additional Example 3: Retail Application
A salesman wants to make a 20% profit on
everything he sells. The equation for the sales
price p is p = 1.2w, where w is wholesale cost.
A. What will be the sales price of a sweater
with a wholesale cost of $48?
p = 1.2(48) The wholesale cost of the sweater before
tax is $48.
p = 57.6
The $48 wholesale sweater will cost the
customer $57.60, so (48, 57.60) is a solution
of the equation.
Pre-Algebra
1-7 Ordered Pairs
Additional Example 3 Continued
A salesman wants to make a 20% profit on
everything he sells. The equation for the sales
price p is p = 1.2w, where w is wholesale cost.
B. What will be the sales price of a jacket with
a wholesale cost of $85?
p = 1.2(85) The wholesale cost of the jacket before tax
is $85.
p = 102
The $85 wholesale jacket will cost the
customer $102, so (85, 102) is a solution of
the equation.
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 3A
In most states, the price of each item is not
the total cost. Sales tax must be added. If
sales tax is 7.5 percent, the equation for total
cost is c = 1.075p, where p is the price before
tax.
A. How much will a $22 item cost after sales
tax?
c = 1.075(22) The price of the item before tax is $22.
c = 23.65
After sales tax, the $22 item will cost $23.65,
so (22, 23.65) is a solution to the equation.
Pre-Algebra
1-7 Ordered Pairs
Try This: Example 3B
In most states, the price of each item is not
the total cost. Sales tax must be added. If
sales tax is 7.5 percent, the equation for total
cost is c = 1.075p, where p is the price before
tax.
B. How much will a $10 item cost after sales
tax?
c = 1.075(10) The price of the item before tax is $10.
c = 10.75
After sales tax, the $10 item will cost $10.75,
so (10, 10.75) is a solution to the equation.
Pre-Algebra
1-7 Ordered Pairs
Lesson Quiz
Determine whether each ordered pair is a
solution for y = 4x  7 .
1. (2, 15) no
2. (4, 9) yes
3. Use the given values to make a table of solutions.
y = 4x  6 for x = 2, 4, 6, 8, and 10
Pre-Algebra
x
4x – 6
y
(x, y)
2
4(2)  6
2
(2, 2)
4
4(4)  6
10
(4, 10)
6
4(6)  6
18
(6, 18)
8
4(8)  6
26
(8, 26)
10
4(10)  6
34
(10, 34)