6
algebra

Determine the value of aa if the lines ax+2y=6ax + 2y = 6 and 3x−y=43x - y = 4 are perpendicular.

A

23\frac{2}{3}

B

−23-\frac{2}{3}

C

66

D

−6-6

Correct Answer: A

Choice A is the correct answer. Product of slopes is -1.

  1. Slope 1: −a/2-a/2.
  2. Slope 2: −3/(−1)=3-3/(-1) = 3.
  3. Condition: (−a/2)×3=−1(-a/2) \times 3 = -1.
  4. Solve: −3a/2=−1→3a=2→a=2/3-3a/2 = -1 \rightarrow 3a = 2 \rightarrow a = 2/3.

💡 Strategic Tip: Or: Slope 2 is 3. Perpendicular slope is -1/3. Set −a/2=−1/3→a/2=1/3→a=2/3-a/2 = -1/3 \rightarrow a/2 = 1/3 \rightarrow a = 2/3.

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

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Linear Functions Set 93