2
algebra

Which equation represents a line perpendicular to 2x+3y=122x + 3y = 12 passing through the origin?

A

y=32xy = \frac{3}{2}x

B

y=−23xy = -\frac{2}{3}x

C

y=−32xy = -\frac{3}{2}x

D

y=23xy = \frac{2}{3}x

Correct Answer: A

Choice A is the correct answer. Find slope, then perpendicular slope.

  1. Original Slope: 2x+3y=12→m=−2/32x + 3y = 12 \rightarrow m = -2/3.
  2. Perp Slope: Negative reciprocal of −2/3-2/3 is 3/23/2.
  3. Intercept: Origin →b=0\rightarrow b=0.
  4. Equation: y=32xy = \frac{3}{2}x.

💡 Strategic Tip: Shortcut: Swap coefficients of x and y, change one sign. 2x+3y→3x−2y2x+3y \to 3x-2y. Then solve for y.

Choice B is incorrect because parallel. Choice C is incorrect because sign error. Choice D is incorrect because reciprocal error.

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Linear Functions Set 92