Compare and Contrast Direct Inverse Variation

12.1: Inverse Variation

[Algebra 1 (X)]

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

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

Step 4: Plot the Ordered Pairs and Connect with Two Curves

0

Product Rule

If , and , are solutions of the same inverse variation, then

and

.

Therefore,

Example 2: Solve for x

If and vary inversely, and when 14.

Step 1: Determine , , ,

7 when

4, find

Step 2: Substitute the values for , , , into the product rule formula

Step 3: Solve for the missing x.

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