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)
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. **
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.