Question 847263
<pre>Tell whether the table represents inverse variation.
If so, write the inverse equation and solve for y 
when x=4. Show work that supports your conclusions.

The Table
Amperes (X)      Ohms  (y)  
   310             .04             
   124              .1
   62               .2 
  15.5              .8

We will start with the inverse equation

{{{y}}}{{{""=""}}}{{{k/x}}}

and substitute in the values and see if the k remains constant:

{{{y}}}{{{""=""}}}{{{k/x}}}

We substitute x = 310 and y = .04 and solve for k

{{{.04}}}{{{""=""}}}{{{k/310}}}

We multiply both sides by 310

{{{12.4}}}{{{""=""}}}{{{k}}}

We substitute x = 124 and y = .1 and solve for k

{{{.1}}}{{{""=""}}}{{{k/124}}}

We multiply both sides by 124

{{{12.4}}}{{{""=""}}}{{{k}}}

So far, so good.  k is so far stayed constant
at 12.4.  But we must check the others too.
Substitute x = 62 and y = .8 and solve for k

{{{.8}}}{{{""=""}}}{{{k/62}}}

Multiply both sides by 62

{{{12.4}}}{{{""=""}}}{{{k}}}

k is still 12.4

Substitute x = 15.5 and y = .8 and solve for k

{{{.8}}}{{{""=""}}}{{{k/15.5}}}

Multiply both sides by 15.5

{{{12.4}}}{{{""=""}}}{{{k}}}

Since the constant k remained constant for
all the given values, we can assume that
the table represents inverse variation.

So we write the inverse equation

{{{y}}}{{{""=""}}}{{{k/x}}}

with k = 12.4

{{{y}}}{{{""=""}}}{{{12.4/x}}} 

and solve for y when x=4.

{{{y}}}{{{""=""}}}{{{12.4/4}}}

{{{y}}}{{{""=""}}}{{{3.1}}}

Edwin</pre>