Learning Objectives:

__Math Tutoring on Solving Direct and Inverse Variation Problems__

To solve **direct variation** problems let us take a look at some real life examples of **direct variation.** For example, the number of hours you work and the amount of your paycheck is an example of **direct variation.** Another example, the amount of weight on a spring and the distance the spring will stretch is an example of **direct variation.** If we are told that **y varies directly as x, **or** y is directly proportional to x**, or we have the equation **y = k x** for some constant **k,** these all mean we have **direct variation **and the number **k** is called the **constant of proportionality.** Also to solve **inverse variation** problems, let us start by taking a look at some real life examples of **inverse variation.** Our first example, the time that a trip takes and the speed traveled would be an example of inverse variation assuming the distance of the trip to be fixed. The next example, the time it takes to spread landscaping rock and the number of people working. Formally, these all represent** inverse variation, y varies as indirectly as x. y is inversely proportional to x, so y = k/x or x * y = k** for some constant **k.** We can also say as the absolute value of one quantity gets bigger, the absolute value of another quantity gets smaller, such as the product is always the same. If this is the case, this would be inverse variation.

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**Hook Questions:**

*1. **How do you find the direct variation?*

*2. **What is direct and inverse variation?*

*3. **What is the meaning of combined variation?*

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