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Tell whether the table represents inverse variation. If so, write the inverse variation...

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loishy | Student, Grade 10 | Salutatorian

Posted June 7, 2013 at 7:56 PM via web

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Tell whether the table represents inverse variation. If so, write the inverse variation equation and solve for y when x=4. Show work that supports your conclusions.

Amperes (x)                 Ohms (y)

    310                             .04

    124                             .1

    62                                .2

    15.5                            .8

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llltkl | College Teacher | Valedictorian

Posted June 8, 2013 at 12:35 AM (Answer #1)

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In an inverse variation, the values of the two variables change in an opposite manner - as one value increases the other decreases.

Here in the given table, the value of y increases as the value of x decreases. So, the table represents inverse variation.

The inverse variation equation is y=`k/x` where k is called the constant of proportionality.

Now, putting any of the corresponding values of x and y of the table in the above equation we get k=12.4

So, when x=4, rewriting the equation we get y=`k/4` =`12.4/4` =3.1(ohms)

This is the required answer.

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 8, 2013 at 2:45 AM (Answer #2)

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The easiest way to check if a table of values represent a function with inverse variation is to find the product of x and y. If y varies inversely with x then the product will be the same. (Note that as x increases y decreases and vice versa, but this does not guarantee that y varies inversely with x. This is a necessary condition, but not sufficient.)

Here the product of x and y is 12.4 for every entry, so y varies inversely with x.

Then `y=k/x` where k is the constant of proportionality. Substituting a known x and y pair we can solve for k: e.g. x=310 y=.04 ==> `.04=k/310 ==> k=12.4` .This is the product of every x,y pair.

So the formula is `y=12.4/x` . If x=4 then `y=12.4/4=3.1`

** Note that if the quotient of y and x is constant, then y varies directly with x. Here y=kx ==> `k=y/x` which is just the slope of the line. **

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