5
algebra

Which equation is equivalent to y=23x4y = \frac{2}{3}x - 4 in standard form?

A

2x3y=122x - 3y = 12

B

2x+3y=122x + 3y = -12

C

3x2y=123x - 2y = 12

D

2x+3y=12-2x + 3y = 12

Correct Answer: A

Choice A is the correct answer. Clear the fraction.

  1. Multiply by 3: 3y=2x123y = 2x - 12.
  2. Rearrange: Subtract 3y3y and add 12? Or subtract 2x2x.
  • 2x+3y=12-2x + 3y = -12.
  • Multiply by -1 to make x positive: 2x3y=122x - 3y = 12.

💡 Strategic Tip: Move xx and yy to the same side. Ax+By=CAx + By = C.

Choice B is incorrect because sign error. Choice C is incorrect because swaps coefficients. Choice D is incorrect because equivalent but usually A is positive.