3

Set 17: Linear Functions (Advanced)

Explanation

Answer: A

Are the lines y=23x+1y = \frac{2}{3}x + 1 and 3x2y=63x - 2y = 6 parallel or perpendicular?

A.

Neither

✓ Correct
B.

Parallel

C.

Perpendicular

D.

Coincident

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Compare slopes. 1. Line 1: m=2/3m = 2/3. 2. Line 2: 2y=3x+6y=32x3-2 y = -3 x + 6 \rightarrow y = \frac{3}{2}x - 3. Slope is 3/23 /2. 3. Compare: 2/32 /3 vs 3/23 /2. They are reciprocals, but NOT negative reciprocals. Signs are the same. 4. Result: Neither. Strategic Tip: For perpendicularity, signs MUST be opposite. Choice B is incorrect because slopes differ. Choice C is incorrect because signs match. Choice D is incorrect.

Key Steps:

The correct answer is Neither

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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