1. Section 5.1 Direct, Inverse, and Joint Variation

2. Do-Now Write a couple sentences to answer the following question…. Why does the moon orbit around the Earth?

3. Types of Variation

4. Direct Variation Two variables, x and y, show direct variation if they are related by a formula y = ax, where a is a constant ≠ 0. This formula implies that as x increases, y also increases based on the value of the constant. Example: Given that y varies directly with x, and that when x = 3, y = 27, write an equation that relates x and y.

5. Applications of Direct Variation Can you think of any formulas that are examples of direct variation, y = ax? Ex: Money spent on an item at the store. Ex: d = rt Ex: E = mc 2 Ex: C = πd Ex: F = ma

6. Inverse Variation

7. Applications of Inverse Variation

8. Direct, Inverse, or Neither? X345678 Y91215182124 X123456 Y5913172125 X12345 Y20106.6754

9. Joint Variation Joint Variation occurs when a quantity varies directly with the product of two or more other quantities. Again, a is a constant in the equation below. z = awxy Z varies jointly with w, x, and y Example: The variable z varies jointly with x and y. Also, z = 60 when x = -4 and y = 5. Write an equation for the relationship. Find z when x = 7 and y = 2.

10. Applications