# College Algebra: Variation

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A series of college algebra lectures. An Introduction to Variation, Direct Proportion, Inverse Proportion.

The following diagrams give the formulas for direct variation and indirect variation functions. Scroll down the page for more examples and solutions.

An Introduction to Variation
An introduction to direct, joint, and inverse variation functions.
Examples:
1. Given y varies directly with x and y = 14 when x = 3.5. Write and graph a variation function.
2. C varies directly as r. C = 7π feet when r = 3.5 feet. Find r when C = 4.5π.
3, A varies jointly as b and h. A = 12m2 when b = 6m and h = 4m. Find b when A = 36m2 and h = 8m.
4. Given y varies inversely as x and y = 3 when x = 8. Write and graph inverse variation function.

Direct Proportion
Examples:
1. Suppose x and y are directly proportional. If x = 24 when y - 18, then what is x when y = 90?
2. The dosage for my medicine is proportional to the patient's weight. It says that a 125-pound person should take 2 teaspoons. How much should a 150-pound person take?
Inverse Proportion
Examples:
1. Suppose x and y are inversely proportional. If x = 24 when y - 18, then what is x when y = 90?
2. It will take 30 hours for 8 graders to grade all the USAMTS papers. If the graders all grade at the same rate, then how many graders do we need to get the grading done in 12 hours?
3. Ohm's Law stated that current and resistance are inversely proportional to the length of the wire. If I wish to double the current flowing through a section of a circuit and all I can change is the length of the wire, then how should I alter the length of the wire?

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