The equation is given as ;
-3+2y - 1/3 x =6
collect like terms as;
2y = 1/3 x + 6 +3
2y = 1/3 x + 9 ----divide each term by 2
y= 1/6 x + 9/2 -----the equation in slope -intercept form
Here you have a slope , m, of 1/6 and y-intercept of 9/2
From the equations given in the answer choices, you can check one by one as;
In A.
-x+6y=27
6y = x+ 27
y=1/6 x + 27/6
y= 1/6 x + 9/2 ------Answer option A is equivalent to our equation so this is not the correct answer.
In B.
6y=27 + x
y=1/6 x + 27/6
y= 1/6 x + 9/2 -------Answer option B is equivalent to our equation so this is not the correct answer.
In C.
2y - x =27
2y = x + 27
y= 1/2 x + 27/2 -------Answer option C is not equivalent to our equation so this is the correct answer
Answer : C : 2y-x=27