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Direct Variation

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Videos, worksheets, solutions, and activities to help Algebra students learn about direct variation or direct proportion. What is direct variation and how to solve direct variation problems?

What is Direct Variation?
We often use the term direct variation to describe a form of dependence of one variable on another. An equation that makes a line and crosses the origin is a form of direct variation, where the magnitude of x increases or decreases directly as y increases or decreases. Direct variation and inverse variation are used often in science when modeling activity, such as speed or velocity.

Some real life examples of direct variation are:
The number of hours you work and the amount of your paycheck
The amount of weight on a spring and the distance the spring will stretch
The speed of a car and the distance traveled in a certain amount of time

How to solve direct variation problems?
In general, if two quantities vary directly, if one goes up the other goes up or down proportionally.
Graphically, we have a line that passed through the origin. The slope is k, which is called the constant of proportionality.

1. Y varies directly with x. y = 54 when x = 9. Determine the direct variation equation and then determine y when x = 3.5.
2. Hooke's Law states that the displacement, d that a spring is stretched by a hanging object caries directly as the mass, m of the object. If the distance is 10 cm when the mass is 3 kg, what is the distance when the mass is 5 kg?
3. Y varies directly with with the square of x. y = 32 when x = 4. Determine the direct variation equation and then determine y when x = 6.
What's the Direct Variation or Direct Proportionality Formula?
Ever heard of two things being directly proportional? Well, a good example is speed and distance. The bigger your speed, the farther you'll go over a given time period. So as one variable goes up, the other goes up too, and that's the idea of direct proportionality. But you can express direct proportionality using equations, and that's an important thing to do in algebra. See how to do that in the tutorial!

Algebra Word Problem: Variation Application
Solving a Variation problem
Direct Variation Models


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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