Ok, let's solve this step by step.
The given equation is 5x - 6y = 9.
In the given options, the equations are in the form of y = mx + c which is a straight line equation. Here, m is the slope of the line and c is the y-intercept.
To compare the given equation with the options, we have to rearrange our equation into the form of y = mx + c.
First, we isolate 6y to one side of the equation:
5x - 9 = 6y.
Next, we divide throughout by 6 to obtain:
y = (5/6)x - 9/6
Simplifying the second part, 9/6 is 1.5, so :
y = (5/6)x - 3/2.
Clearly, none of the options match the re-arranged equation form. So none of the options are equivalent to the given equation 5x - 6y = 9.
So, the final answer is that none of the options are equivalent to the initial condition.