Direct Variation Talking about the relationship between variables in a new way!!! Fun, Huh?

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Direct Variation Learn to recognize direct variation and identify the constant of proportionality.

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Presentation transcript:

Direct Variation Talking about the relationship between variables in a new way!!! Fun, Huh?

Many relationships in every day life involve a relationship between measurable quantities Your pay is related directly to the hours you work, given a fixed hourly wage The distance you travel is related directly to the hours you drive, given a fixed rate of speed The number of words typed is related directly to the time spent typing, given a fixed number of words per minute. The amount of money that a magazine pays for an article is related directly to the number of words, given a fixed amount of money paid per word The volume of a dry gas is related directly to its temperature, given a fixed pressure

There are many ways to say the same thing y is related directly to x x and y vary directly y varies directly as x y is directly proportional to x y is dependent on x

Constant of variation Note that in each of the preceding examples the GIVEN is constant This is called the constant of variation The variable k is assigned to this constant The equation y = kx is the mathematical way to say the y is related directly to x.

Sample problem The variables x and y vary directly. When x = - 3 and y = -30. Write an equation that relates x and y Find the value of y when x = 8

Solution Recall y = kx. Now substitute numbers in for what you know. -30 = k (-3) 10 = k Using that information you can write the equation that relates x and y: y = 10x

Now we can solve that equation when x = 8 y = 10 x y = 10(8) y= 80

Problems of direct variation can also be solved using proportions

Sample

One more problem The forearm lengths and body heights in inches of five people are shown in the table. Write a direct variation model that relates body length B to forearm length F B = 7.5 F Estimate the body length of a person whose forearm length is 10 inches 75 in F B