compare and contrast direct inverse...
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12.1: Inverse Variation
HCPS III: Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS:
Understand various types of patterns and functional relationships.
Benchmark MA.AI.9.2: Compare and contrast the concepts of direct and inverse variation of a relation.
Goals: Graph inverse variations.
Solve problems involving inverse variations.
Compare and Contrast Direct & Inverse Variation
is the constant of variation
[Algebra 1 (X)]
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Inverse Variation
Example 1: Graph an Inverse Variation
Find an equation that relates and such that and vary inversely. Then, graph the inverse variation.
6, 15 Inverse Variation Equation
Step 1: Find k
Step 2: Write the Equation
Graph of Inverse Variation
Step 3: Table of Values (choose x‐values that k is divisible by)
x y 0
Step 4: Plot the Ordered Pairs and Connect with Two Curves
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Product Rule
If , and , are solutions of the same inverse variation, then ⋅ and ⋅ .
Therefore,
Example 2: Solve for x
If and vary inversely, and 7 when 4, find when 14.
Step 1: Determine , , ,
Step 2: Substitute the values for , , , into the product rule formula Step 3: Solve for the missing x.