Lesson 6-9: Variation Objective: Students will:

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Lesson 6-9: Variation Objective: Students will: Find the constant of variation and setup direct and inverse variation equations Use variation equations to solve problems

Direct Variation Equations: or Why direct? Take or , where k = 2 If y goes up, x must go up y and x move the same → direct “k” is the constant of variation – must stay constant

Inverse Variation Equations: or Inverse → opposite → if y goes up, x must go down… Choosing Identify the variables Ask: if the one value increases, what will the other do? increase also → direct decrease → inverse

Example 1 The force applied to a spring causes the length to increase. 8 pounds makes the spring 4 inches. Find k and write a general equation. Example 2 A theater makes $900 with 200 people. Find k, write a general equation, and how much would it make with 500 people.