Answer:
A, B, C, E
Step-by-step explanation:
You want to know the equations on the list that have the same graph as 2x+3y=12.
Comparing equations
Equations are most easily compared when they are written in the same form. Here, there is a mix of "standard form", "slope-intercept form", and "point-slope form." We can convert all of these to slope-intercept form to make the comparison.
Equations
Reference equation
2x +3y = 12 ⇒ 3y = -2x +12 ⇒ y = -2/3x +4
A.
y -2 = -2/3(x -3) ⇒ y = -2/3x +2 +2 ⇒ y = -2/3x +4 . . . equivalent
B.
x +3/2y = 6 ⇒ 3/2y = -x +6 ⇒ y = -2/3x +4 . . . equivalent
This is the original equation divided by 2.
C.
-2x -3y = -12 ⇒ -2x +12 = 3y ⇒ y = 2/3x +4 . . . equivalent
This is the original equation multiplied by -1.
D.
y -2 = -2/3x +4 ⇒ y = -2/3x +6 . . . not equivalent
E.
y = -2/3x +4 . . . equivalent
