## Tutoring on Direct Variation

Learning Objectives:

#### Understand Direct Variation and Hooke's Law.

Math Tutoring on Direct Variation

For Direct Variation, the following statement is the same or equivalent. 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.
So because of this equation here, in general, if two quantities vary directly, if one goes up, let us say
x, then the other will go up or down proportionally based upon the value of k. Graphically this equation should remind us of y = mx where the y intercept would be 0. We have a line passing through the origin with a slope of k. Now, it is important to mention that most real life applications occur in the first quadrant where x and y are positive, but it doesn't necessarily have to be the case every time.
A well-known example,
Hooke's law is a principle of physics that states the force f needed to stretch or compress a spring by some distance, s, is proportional to that distance. Since f is proportional to s, we can use the direct variation equation f = ks to represent this relationship, where f is the force, k is the spring constant and s is the distance the spring is stretched.

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Hook Questions:

 1.    What is meant by Direct Variation? 2.    What is the role of Constant of Proportionality? 3.    How does Hook's Law is associated with Direct Variation?

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