Question

Find the constant of variation k for the direct variation.

x f ( x )
0 0
3 6
4 8
7 14



A.) k = –2




B.) k = 0.5


C.) k = 2.5


D.) k = 2

Answer 1

The correct option is D.

Explanation:

It is given that x is directly proportional to f(x) and constant of variation is k.

`f(x)\propto x`

`f(x)=kx`

Therefore k is the slope.

Slope formula is

`k=(y_2-y_1)/(x_2-x_1)`

From the table the two points are (0,0) and (3,6).

`k=(6-0)/(3-0)=(6)/(3)=2`

Therefore the value of constant of variation is 2 and option D is correct.