Set 12: Linear Functions

Explanation

Answer: A

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

$2x - 3y = 12$

✓ Correct

$2x + 3y = -12$

$3x - 2y = 12$

$-2x + 3y = 12$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Clear the fraction. 1. Multiply by 3: $3y = 2 x - 12$ . 2. Rearrange: Subtract $3y$ and add 12? Or subtract $2x$ . - $-2 x + 3 y = -12$ . - Multiply by -1 to make x positive: $2x - 3 y = 12$ . Strategic Tip: Move $x$ and $y$ to the same side. $Ax + By = C$ . 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.

Key Steps:

•

The correct answer is $2x - 3y = 12$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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