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Which of the following equations has the same graph as 2x + 3y = 12?
Select all that apply.

A. y-2=-2/3(x-3)
B. x+3/2y=6
c. -2x-3y = - 12
D. y-2=-2/3x+4
E. y=-2/3x+4

Sagot :

sqdancefan

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

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