Question

Which explains whether or not the values in the table represent a direct variation? x 4 6 10 20 y 1 1.5 2.5 5 The table represents a direct variation because the values are proportional. The table represents a direct variation because the values are nonproportional. The table does not represent a direct variation because the values are proportional. The table does not represent a direct variation because the values are nonproportional.

Answer 1

Answer: A The table represents a direct variation because the values are proportional.

Explanation:

Answer 2

Option A is correct.

The table represents a direct variation because the values are proportional.

Explanation:

The direct variation says that:

`y \propto x`

then; the equation is of the form :
`y =kx` where k is the Constant of Variation.

Consider any values of x and y from the table, to solve for k;

Let x = 10 and y = 2.5

then;

`2.5 = 10k`

Divide both sides by 10 we have;

`k = (2.5)/(10) = (25)/(100) = (1)/(4)`

Then the equation becomes:

`y =(1)/(4)x`

Therefore, the table represents a direct variation because the values are proportional.