2

Set 8: Linear Functions (Intermediate)

Explanation

Answer: A

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}

✓ Correct
B.

−23-\frac{2}{3}

C.

66

D.

−6-6

Detailed Explanation

Choice A is correct. 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=2/3-3 a/2 = -1 \rightarrow 3 a = 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.

Key Steps:

•

The correct answer is 23\frac{2}{3}

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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