5-6 inverse variation warm up warm up lesson presentation lesson presentation problem of the day...

5-6 Inverse Variation

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

5-6 Inverse Variation

Warm Up

Find each product or quotient.

1. 3(12) 2. 6(75)

3. 4.

5. Solve 6x = 54.

36 450

27 9

x = 9

81 3

55 6

1 6

5-6 Inverse Variation

Problem of the Day

The directions say to mix 2 cups of red paint for every 5 cups of white paint. Amos has 7 cups of red paint. How much white paint does he need?

17.5 cups

5-6 Inverse Variation

MA.7.G.1.5 Distinguish direct variation from other relationships, including inverse variation.

Sunshine State Standards

5-6 Inverse Variation

Vocabulary

inverse variation

5-6 Inverse Variation

Inverse variation is a relationship between two variables that can be written in the form y =k/x or xy = k, where k is a nonzero constant and x 0.

In an inverse variation, the product of x and y is constant.

5-6 Inverse Variation

Tell whether each relationship is an inverse variation, a direct variation or neither. Explain.

Additional Example 1A: Identifying an Inverse Variation

Find y/x for each pair. x 4 6 8

y 12 18 24

The data represents a direct variation where k = 3.

5-6 Inverse Variation

Tell whether each relationship is an inverse variation, a direct variation or neither. Explain.

Additional Example 1B: Identifying an Inverse Variation

Find the product xy.x 3 4 5

y 40 30 24

The data represents a inverse variation where k = 120.

3(40) = 120 4(30) = 120 5(24) = 120

5-6 Inverse Variation

Check It Out: Example 1A

x 2 4 8

y 40 20 10

The product xy is constant, so the relationship is an inverse variation, and k = 80.

Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

5-6 Inverse Variation

Check It Out: Example 1B

x 4 7 10

y 25 14 10

The product xy is not constant. The quotient is not constant. The relationship is neither an inverse variation nor a direct variation.

Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

yx

5-6 Inverse Variation

Eliza is building a rectangular patio. She has cement to cover 72 square feet. Write an inverse variation equation to find the width of the patio for lengths 4, 6, and 8 feet.

Additional Example 2: Application

Use xy = k.

Substitute for x and k.

An inverse variation equation is xy = 72. Eliza can build a 4 ft by 18 ft, 6 ft by 12 ft, or 8 ft by 9 ft patio.

xy = k

4y = 72

y = 18

xy = k

6y = 72

y = 12

xy = k

8y = 72

y = 9

5-6 Inverse Variation

A pizzeria makes rectangular pizzas. One ball of dough can cover 36 square inches.Write an inverse variation equation to represent the length of the pans for widths3, 4, and 6 inches.

Check It Out: Example 2

xy = 36; the pizza pans are 3 inches by 12 inches, 4 inches by 9 inches and 6 inches by 6 inches.

5-6 Inverse Variation

Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain.

Additional Example 3: Identifying a Graph of an Inverse Variation

Identify points on the graph. Use the equation xy = k.

(1)2= 2, (2)3 = 6

The values of k are not constant. The graph does not represent an inverse variation.

5-6 Inverse Variation

Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain.

Additional Example 3 Continued

Identify points on the graph. Use the equation y/x = k.

1/1 = 1, 2/1 = 2

The values of k are not constant. The graph does not represent an direct variation.

The graph is neither.

5-6 Inverse Variation

Check It Out: Example 3

direct variation; is constant; the graph passes through (0, 0)

Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain.

yx

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5-6 Inverse Variation

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

5-6 Inverse Variation

Lesson Quiz: Part I

neither

Tell whether each relationship represents an inverse variation, a direct variation, or neither. Explain.

direct

1.

2.

3.

inverse

5-6 Inverse Variation

Lesson Quiz: Part II

4. A company will donate $100,000 to local schools. Write an inverse variation equation to represent the money that will be donated. Use the equation to find the amount of money donated for 4, 8, and 10 schools.

xy = 100,000; $25,000, $12,5000, $10,000

5-6 Inverse Variation

1. Tell whether each relationship represents an inverse variation, a direct variation, or neither.

A. inverse

B. direct

C. neither

Lesson Quiz for Student Response Systems

x 10 8 4

y 4 5 10

5-6 Inverse Variation

2. Tell whether each relationship represents an inverse variation, a direct variation, or neither.

A. inverse

B. direct

C. neither

Lesson Quiz for Student Response Systems

x 10 20 5

y 40 80 20