Answer:
Option C is correct.
Constant of variation k = -0.5
Step-by-step explanation:
The direct variation says that:
[tex]y \propto x[/tex]
then, the equation is of the form: [tex]y =kx[/tex] .....[1] where k is the constant of variation.
Given the table:
x f(x)=y
0 0
2 -1
4 -2
7 -3.5
Consider any values from the tables
x = 4 and y=f(x) = -2
Substitute these values in equation [1] we have;
[tex]-2 = 4k[/tex]
Divide both sides by 4 we get;
[tex]k = -\frac{2}{4} = -0.5[/tex]
Therefore, the constant of variation is, -0.5
