Direct and inverse variation
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This document defines and provides examples of direct and inverse variation. Direct variation describes a proportional relationship where two variables increase or decrease together. Inverse variation describes an inverse proportional relationship where one variable increases as the other decreases. The document also gives examples of solving direct and inverse variation problems by setting up and solving proportions.
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Direct and inverse variation
- 1. DIRECT AND INVERSE VARIATION Some Examples to Help You on Your Mastery Assignment
- 2. Direct Variation ◦ Describes the relationship between two variables who either both increase or both decrease ◦ As one variable increases, so does the other ◦ As one variable decreases, so does the other ◦ As the temperature goes up, so does my electric bill because I pay for AC ◦ As I make more money, more taxes are taken out of my paycheck
- 3. Inverse Variation ◦ Describes the relationship between two variables who behave in opposite ways ◦ As one variable increases, the other variable decreases ◦ As one variable decreases, the other variable increases ◦ The less gas that is available in the United States, the more each gallon costs ◦ As the number of people in a room increases, the amount of oxygen to breathe decreases
- 4. The variables x and y are directly proportional to one another. If x = 4 when y = 12, find y when x = 8. ◦ x/y = x/y ◦ 4/12 = 8/y ◦ 4y = 96 ◦ y = 24
- 5. The variables x and y are inversely proportional to one another. If x = 4 when y = 12, find y when x = 8. ◦ xy = xy ◦ 4(12) = 8y ◦ 48 = 8y ◦ y = 6