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3-1 Ordered Pairs
Problem of the Day
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
3-1 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 12 players. Find the cost for a set of jerseys for each team.
Let y be the total cost of a set of jerseys and x be the number of jerseys needed.
3-1 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
3-1 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).
3-1 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
3-1 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.
3-1 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.
3-1 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.
3-1 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
3-1 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)
3-1 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
3-1 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
3-1 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.
3-1 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.
3-1 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.
3-1 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.
3-1 Ordered Pairs
Lesson Quiz: Part IDetermine whether each ordered pair is a solution of y = 4x – 7.
1. (2, 15) 2. (4, 9)
3. Use the given values to make a table of
solutions. y = 4x 6 for x = 2, 4, 6, 8, and 10
yesno
(10, 34)344(10) – 610
(8, 26)264(8) – 68
(6, 18)184(6) – 66
(4, 10)104(4) – 64
(2, 2)24(2) – 62
(x, y)y4x – 6 x
3-1 Ordered Pairs
Lesson Quiz: Part II
4. A plumbing company charges $50 for a service
call and $15 per hour. They went on a 3-hour
job. How much did the company earn?
c = 15n + 50; $95
3-1 Ordered Pairs
1. Which of the following ordered pairs is the solution of y = 6x – 9?
A. (1, 3)
B. (2, 3)
C. (3, 2)
D. (3, 7)
Lesson Quiz for Student Response Systems
3-1 Ordered Pairs
2. Which of the following ordered pairs is NOT the solution of y = 4x + 7?
A. (4, 23)
B. (5, 20)
C. (1, 11)
D. (3, 19)
Lesson Quiz for Student Response Systems
3-1 Ordered Pairs
3. Use the given values to identify the table of solutions.
y = 6x – 4 for x = 1, 3, 5, 7, and 9
A. B.
Lesson Quiz for Student Response Systems
3-1 Ordered Pairs
4. The water level in a tank is 17 feet. Due to the heavy rainfall, the water level increases at the rate of 7 feet per hour. What will be the water level in the tank after 5 hours?
A. L = 17n + 17; 102 ft
B. L = 17n + 7; 92 ft
C. L = 7n + 17; 52 ft
D. L = 7n + 7; 42 ft
Lesson Quiz for Student Response Systems