Answer:
The correct option is d.
Step-by-step explanation:
If y varies directly with x, then y is directly proportional to x.
[tex]y\propto x[/tex]
[tex]y=kx[/tex] .... (1)
Where, k is constant of variation.
From the given table it is clear that the value of y is -4 at x=-2.
Put x=-2 and y=-4 in equation (1).
[tex]-4=k(-2)[/tex]
Divide both sides by -2.
[tex]2=k[/tex]
The value of k is 2. Put this value in equation (1), to find the relation between x and y.
[tex]y=2x[/tex]
At x=-4,
[tex]y=2(-4)=-8[/tex]
At x=-16,
[tex]y=2(-16)=-32[/tex]
All the points of the table satisfy the equation. It means y is directly proportional to x, the constant of variation is 2 and required equation is y=2x.
Hence option d is correct.
