Question

Which best describes the function represented by the table?

direct variation; k = 2/5
direct variation; k = 5/2
inverse variation; k = 10
direct variation; k = 1/10

Answer 1

The second answer should be correct. "direct variation; k = 5/2"

Answer 2

Option B is correct.

direct variation; k = 5/2

Explanation:

The Direct variation says:

`y \propto x`

then the equation is of the form:
`y = kx` ......[1] where k is the constant of variation.

From the given table:

Consider x = -2 and y = -5

Substitute these in [1] to solve for k;

`-5 = -2k`

or

5 = 2k

Divide both sides by 2 we get;

`k = (5)/(2)`

⇒ the equation becomes:
`y = (5)/(2)x`

Check:

Take x = 4 and y = 10;

`y = (5)/(2)x`

`10 = (5)/(2) * 4`

`10 = 5 * 2`

10 = 10 True

Therefore, the direct variation ;
`k = (5)/(2)` best describe the function represented by the table