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Determine in the data in the table is direct, inverse

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or joint variation. Then identify the equation that

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represents the relationship. So lets just think about

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direct , inverse of joint variation means.

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Direct variation - if y varies directly with x

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if y = constant multiple of x. if you divide both sides by x

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y / x = k, so the ratio betwen y & x is some constant

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and you can go the other way around x = consta x ynt

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or x/y = k these are not the same k

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I am saying these are constant relationship

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inverse relationship is some degree the opposite.

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If x increases y should increase in direct variation.

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if you increase x by some factor x going up by 3x

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then y should also increase by the same factor 3

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inverse variation you have y being some constant over

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1/x; y = k x 1/x

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if you multiply both sides by x then you have x.y = k

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If you increase x they y will go down

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and if you take x and increase by a factor of 3

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you are decreasing this by a whole factor of 1/3

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so then you are going to reduce y by 1/3

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now finally they talk about joint variation

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joint variation deals with more than one variable

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if area of a rectangle = length x breadth, this is

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a example of joint variation. area depends on two variables

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joint variation deals with more than two variables

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as x goes from 1 to 2, y is going from 12 to 6

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if x is going up by 2, y is oming down by 1/2

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as x goes from 1 to 3, y is multipled by 1/3

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this is not direct variation as x increases

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y is decreasing this is going to be inverse variation

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when x increases by a certain factor,

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y is decreasing by the same factor.

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if x is increasing by 3, y is decreasing by 1/3 of the

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original value. So we have inverse variation in place.

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They ask identify the equation that represents this relationship

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we know that inverse variation the product of x and y

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needs to be some constant. let me make another

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column x times y, 1x12 = 12; 2x6=12; 3x4=12; 4x3=12

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clearly in every situation x.y = 12

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so the equation that represents the relation ship is

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x.y = 12