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Notes 25. Inverse Variation. Vocabulary. Inverse variation- 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. - PowerPoint PPT Presentation
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Inverse Variation
*Notes 25
Vocabulary
Inverse variation- 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.
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.
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.
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
Check It Out: Example 1A
x 2 4 8
y 40 20 10
Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.
Check It Out: Example 1B
x 4 7 10
y 25 14 10
Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.
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
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
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.
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.
Check It Out: Example 3Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain.
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