8
algebra

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

A

Neither

B

Parallel

C

Perpendicular

D

Coincident

Correct Answer: A

Choice A is the correct answer. Compare slopes.

  1. Line 1: m=2/3m = 2/3.
  2. Line 2: 2y=3x+6y=32x3-2y = -3x + 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.