2-1 Ordered Pairs Lesson Presentation Lesson Presentation
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2-1 Ordered Pairs
Lesson PresentationLesson Presentation
2-1 Ordered Pairs
Practice Problems
Solve.
x = 27
a = 7
n = 17
c = 13
y = 3E. 17y + 7 = 58
D. 3c – 7 = 32
C. 7 + n = 24
B. 5 = a – 2
A. x – 8 = 19
2-1 Ordered Pairs
Practice Problem F
A moving van travels 50 miles per hour. Use the equation y = 50x, where x represents the number of hours. How far will the van travel in 4.5 hours?
225 miles
2-1 Ordered Pairs
Learn to write solutions of equations in two
variables as ordered pairs.
2-1 Ordered Pairs
Vocabulary
ordered pair
2-1 Ordered Pairs
The company that makes team uniforms for a soccer league charges a $20 fee for team artwork and $10 for each jersey. Dominic’s team has 14 players, and Alyssa’s team has 12players. Find the cost for a set of jerseys for each team.
Let y be the total cost of a set of jerseys and xbe the number of jerseys needed.
2-1 Ordered Pairs
y = $20 + $10 • x
Dominic’s team:
= + •
Alyssa’s team:
y = $20 + ($10 • 14)
y = $20 + ($10 • 12)
total cost of jerseys $20 $10 # of jerseys
y = $160
y = $140
2-1 Ordered Pairs
An ordered pair (x, y) is a pair of numbers that can be used to locate a point on a coordinate plane. A solution of a two-variable equation can be written as an ordered pair.
The ordered pair (14, 160) is a solution because 160 = $20 + ($10 • 14).
The ordered pair (12, 140) is a solution because 140 = $20 + ($10 • 12).
2-1 Ordered Pairs
Determine whether each ordered pair is a solution of y = 4x – 1.
Additional Example 1A: Deciding Whether an Ordered
Pair Is a Solution of an Equation
(3, 11)
y = 4x – 1
11 = 4(3) – 1?
Substitute 3 for x and 11 for y.
11 = 11�
(3, 11) is a solution.
Simplify.
The order in which a solution is written is important. Always write x first, then y.
Helpful Hint
2-1 Ordered Pairs
(10, 3)
y = 4x – 1
3 = 4(10) – 1?
Substitute 10 for x and 3 for y.
3 ≠ 39 �
(10, 3) is not a solution.
Determine whether each ordered pair is a solution of y = 4x – 1.
Additional Example 1B: Deciding Whether an Ordered
Pair Is a Solution of an Equation
Simplify.
2-1 Ordered Pairs
Determine whether each ordered pair is a solution of y = 5x + 3.
Check It Out: Example 1A
(7, 38)
y = 5x + 3
38 = 5(7) + 3?
Substitute 7 for x and 38 for y.
38 = 38?
�
(7, 38) is a solution.
2-1 Ordered Pairs
Determine whether each ordered pair is a solution of y = 5x + 3.
Check It Out: Example 1B
(9, 17)
y = 5x + 3
17 = 5(9) + 3?
Substitute 9 for x and 17 for y.
17 = 48?
�
(9, 17) is not a solution.
2-1 Ordered Pairs
Use the given values to make a table of solutions.
Additional Example 2A: Creating a Table of Ordered
Pair Solutions
y = x + 3 for x = 1, 2, 3, 4
x x + 3 y (x, y)
1
2
3
4
1 + 3 4 (1, 4)
2 + 3 5 (2, 5)
3 + 3 6 (3, 6)
4 + 3 7 (4, 7)
A table of solutions can be set up vertically or horizontally.
Helpful Hint
2-1 Ordered Pairs
Use the given values to make a table of solutions.
Additional Example 2B: Creating a Table of Ordered
Pair Solutions
n = 6m – 5 for m = 1, 2, 3
6(1) – 5 6(2) – 5 6(3) – 5
1 7 13
(1, 1) (2, 7) (3, 13)
m 1 2 3
6m – 5
n
(m, n)
2-1 Ordered Pairs
Use the given values to make a table of solutions.
y = x + 6 for x = 1, 2, 3, 4
x x + 6 y (x, y)
1
2
3
4
1 + 6 7 (1, 7)
2 + 6 8 (2, 8)
3 + 6 9 (3, 9)
4 + 6 10 (4, 10)
Check It Out: Example 2A
2-1 Ordered Pairs
Use the given values to make a table of solutions.
n = 8m – 2 for m = 1, 2, 3, 4
30
8(1) – 2 8(2) – 2 8(3) – 2
6 14 22
(1, 6) (2, 14) (3, 22) (4, 30)
8(4) – 2
m 1 2 3
8m – 2
n
(m, n)
4
Check It Out: Example 2B
2-1 Ordered Pairs
A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost.
Additional Example 3A: Consumer Math Application
What will be the sales price of a sweater with a wholesale cost of $48?
p = 1.2(48)
p = 57.6
The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation.
The wholesale cost of the sweater before tax is $48. Multiply.
2-1 Ordered Pairs
Additional Example 3B: Consumer Math Application
What will be the sales price of a jacket with a wholesale cost of $85?
p = 1.2(85)
p = 102
The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation.
The wholesale cost of the jacket before tax is $85. Multiply.
A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost.
2-1 Ordered Pairs
In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax.
Check It Out: Example 3A
How much will a $22 item cost after sales tax?
c = 1.075(22)
c = 23.65
After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation.
The price of the item before tax is $22. Multiply.
2-1 Ordered Pairs
In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax.
Check It Out: Example 3B
How much will a $10 item cost after sales tax?
c = 1.075(10)
c = 10.75
After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation.
The price of the item before tax is $10. Multiply.
2-1 Ordered Pairs
Assignments:
1.) Ch. 2-1 Review Packet Mon. 11-25
2.) Pg. 52 (1-24) Tues. 11-26
3.) 3 graphing sheets Wed. 11-27
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