How can I determine any table for x and y to be a direct variation of inverse variation? example:

Question

|x=1  2  3  4 |

|y=2  4  6  8 |

Answer 1

If for each x the associated y = kx, and k is always the same regardless of which (x,y) pair that you examine, then this is direct variation.

 

Now let's consider:

x: 1  2    3       4  

y: 1  ½  1/3   0.25

 

If for each x the associated y = k/x & k is always the same for each (x,y) pair, then it's inverse variation.

Answer 2

If y varies directly with x then

y = kx

 

If y varies inversely with x then

y = k/x

 

In each case k is a constant... the

constant of variation

 

in your table each value of y is

equal to twice the corresponding

value of x:

 

y = 2x

 

This is a direct variation of

form y = kx with k = 2