Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

3y=-7x-18
A. yes; 3
B. yes; -7
C. no
D. yes; 7/3

To determine whether y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.

The given equation is 3y = -7x - 18.

We can solve this equation for y by dividing both sides by 3:

y = (-7/3)x - 6.

This equation does not match the form y = kx, so y does not vary directly with x.

Therefore, the answer is C. no.

To determine whether y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.

Looking at the given equation: 3y = -7x - 18

We can rearrange it to isolate y:

y = (-7x - 18) / 3

Now let's compare it with the form y = kx:

The given equation can be written in the form y = (-(7/3))x - 6

Comparing the equations, we can see that the constant of variation, k, is -(7/3).

Therefore, the answer is D. yes; 7/3