pre-algebra 1-7 ordered pairs 1-7 ordered pairs pre-algebra warm up warm up problem of the day...

Pre-Algebra

1-7 Ordered Pairs1-7 Ordered Pairs

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

1-7 Ordered Pairs

Warm UpSolve.

x = 27

a = 7n = 17

c = 13

y = 3

Pre-Algebra

1-7 Ordered Pairs

5. 17y + 7 = 58

4. 3c 7 = 32

3. 7 + n = 24

2. 5 = a 21. x 8 = 19

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

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:

Price of banner

= $8 + $1 • Number of letters in name

For Dowen’s banner:

x = 7, y = 8 + 7 or y = 15

x = 5, y = 8 + 5 or y = 13

Pre-Algebra

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) Ordered pair

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 4x – 1.

Additional Example 1A: Determining If an Ordered Pair Is a Solution of an Equation

A. (3, 11)

y = 4x – 1

11 = 4(3) – 1?

Substitute 3 for x and 11 for y.

11= 11 ?

(3, 11) is a solution.

A solution since 11=11.

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 4x – 1.

Additional Example 1B: Determining If an Ordered Pair Is a Solution of an Equation

B. (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.

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 4x – 1.

Additional Example 1C: Determining If an Ordered Pair Is a Solution of an Equation

C. (11, 43)

y = 4x – 1

43 = 4(11) – 1 ?

Substitute 11 for x and 43 for y.

43 = 43?

(11, 43) is a solution.

A solution since 43 = 43.

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 5x + 3.

Try This: Example 1A

A. (7, 38)

y = 5x + 3

38 = 5(7) + 3?

Substitute 7 for x and 38 for y.

38 = 38 ?

(7, 38) is a solution.

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 5x + 3.

Try This: Example 1B

B. (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.

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair is a solution of y = 5x + 3.

Try This: Example 1C

C. (10, 53)

y = 5x + 3

53 = 5(10) + 3?

Substitute 10 for x and 53 for y.

53 = 53 ?

(10, 53) is a solution.

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of solutions.

Additional Example 2A: Creating a Table of Ordered Pair Solutions

A. y = 7x for x = 1, 2, 3, 4

x 7x y (x, y)

1

2

3

4

7(1) 7 (1, 7)

7(2) 14 (2, 14)

7(3) 21 (3, 21)

7(4) 28 (4, 28)

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of solutions.

Additional Example 2B: Creating a Table of Ordered Pair Solutions

B. n = 6m – 5 for m = 1, 2, 3, 4

19

6(1) – 5 6(2) – 5 6(3) – 5

1 7 13

(1, 1) (2, 7) (3, 13) (4, 19)

6(4) – 5

m 1 2 3

6m – 5

n

(m, n)

4

Pre-Algebra

1-7 Ordered Pairs

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

2

3

4

6(1) 6 (1, 6)

6(2) 12 (2, 12)

6(3) 18 (3, 18)

6(4) 24 (4, 24)

Try This: Example 2A

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of solutions.

B. 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

Try This: Example 2B

Pre-Algebra

1-7 Ordered Pairs

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.

Additional Example 3: Retail Application

A. 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.

Pre-Algebra

1-7 Ordered Pairs

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.

Additional Example 3 Continued

B. What will be the sales price of a jacket with a wholesale cost of $85?

p = 1.2(85)

p = 102

The $85 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.

Pre-Algebra

1-7 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 percent, the equation for total cost is c = 1.075p, where p is the price before tax.

Try This: Example 3A

A. 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.

Pre-Algebra

1-7 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 percent, the equation for total cost is c = 1.075p, where p is the price before tax.

Try This: Example 3B

B. 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.

Pre-Algebra

1-7 Ordered Pairs

Lesson QuizDetermine whether each ordered pair is a solution for 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

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)