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Ch. 11Vocabulary 5) Inverse variation
6.) constant of variation (for an inverse variation)
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11-6A Inverse Variation Algebra 1
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The variables x and y vary directly if, for a constant k,
USING DIRECT AND INVERSE VARIATION DIRECT VARIATION The variables x and y vary directly if, for a constant k, y x = k, or y = kx, k 0.
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The variables x and y vary inversely, if for a constant k,
USING DIRECT AND INVERSE VARIATION INDIRECT VARIATION The variables x and y vary inversely, if for a constant k, k x = y, or xy = k, k 0.
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MODELS FOR DIRECT AND INVERSE VARIATION
USING DIRECT AND INVERSE VARIATION MODELS FOR DIRECT AND INVERSE VARIATION DIRECT VARIATION INVERSE VARIATION k x = y y = kx k > 0 k > 0
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Example 1 When x is 3, y is 12. Find an equation that x and y vary inversely.
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Example 2 Does the date in each table represent a direct variation or an inverse variation? For each, write an equation to model the data. A.) B.) x Y 4 -12 6 -8 8 -6 x y 4 -12 6 -18 8 -24
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An 8 sliced pizza is share equally by a group of friends.
Example 3 Tell whether each situation represents a direct variation or inverse variation. Explain your reasoning. An 8 sliced pizza is share equally by a group of friends.
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Assignment
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Example 3 Decide if the data in the table show direct or inverse variation. Write an equation that relates the variables. #37 on pg. 660
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Compare the direct variation model and the inverse
Comparing Direct and Inverse Variation Compare the direct variation model and the inverse variation model you just found using x = 1, 2, 3, and 4. SOLUTION Plot the points and then connect the points with a smooth curve. Direct Variation: the graph for this model is a line passing through the origin. Direct y = 2x Inverse Variation: The graph for this model is a curve that gets closer and closer to the x-axis as x increases and closer and closer to the y-axis as x gets close to 0. Inverse 8 x y =
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Example 2 Make a table of values for x = 1, 2, 3 and 4. Use the table to sketch a graph. Decide whether x and y vary directly or inversely. #33 pg. 659
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Compare the direct variation model and the inverse
Comparing Direct and Inverse Variation Compare the direct variation model and the inverse variation model you just found using x = 1, 2, 3, and 4. Make a table using y = 2x and y = 8 x SOLUTION 8 x y = y = 2x 1 2 3 4 6 Direct Variation: k > 0. As x increases by 1, y increases by 2. Inverse Variation: k > 0. As x doubles (from 1 to 2), y is halved (from 8 to 4).
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