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Direct/Inverse Variations

Direct/Inverse Variations . Direct Variation .

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Direct/Inverse Variations

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  1. Direct/Inverse Variations

  2. Direct Variation Direct variation is  two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. Given two variables x and y, y is (directly) proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k. We also say that one of the quantities is proportional to the other. Direct variation can also be found when the x variable and y variable on a data table or graph both increase. For example: The equation for direct variation is: Y=KX Or Y/X=K These variables stand for: X- the X axis or variable Y- the Y axis or variable K- the constant of variation X 1 2 3 2 4 6 Y

  3. Inverse Variation Inverse variation is when two variables are inversely proportional, or varying inversely, if one of the variables is directly proportional with the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. It follows that the variable y is inversely proportional to the variable x if there exists a non-zero constant k. Inverse variation can also be found when one of the variables in a data table or graph is increasing while the other is decreasing. For example: The equation for inverse variation is: Y=K/X Or K=XY These variables stand for: X- the X axis or variable Y- the Y axis or variable K- the constant of variation X 5 6 7 4 3 2 Y

  4. Examples Direct Variation If Y varies directly with X, an Y=28 when X=7, find X when Y=52 To solve you must use the equation Y/X=K Soo.. 28/7=52/X cross multiply the numbers 28X=364 divide 364 by 28 and you get 13 as your answer Inverse Variation The volume V of gas varies inversely to the pressure P. The volume of gas is 200 cm³ under the pressure of 32 kg/cm². What will be its volume under pressure of 40 kg/cm²? To solve you must use the equation k=YX Soo.. (200)(32)=X(40) multiply the numbers 6400=40x divide 6400 by 40 and you get 160 as your answer

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