Question

Question
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line.

4x+3y=31 3x+4y=8 3x+4y=12 -4x+3y=-1



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Parallel Perpendicular Neither

Answer 1

First line: 4x+3y=31 ⇒ y = -(4/3)x + 31/3, slope = -4/3.

Other lines:
- 3x+4y=8 ⇒ y = -(3/4)x + 2, slope = -3/4
- 3x+4y=12 ⇒ y = -(3/4)x + 3, slope = -3/4
- -4x+3y=-1 ⇒ y = (4/3)x - 1/3, slope = 4/3

Parallel to 4x+3y=31 would need slope -4/3 — none of the three have that.
Perpendicular would need slope 3/4 — none of the three have that.

So:
- Parallel: (none)
- Perpendicular: (none)
- Neither: 3x+4y=8 ; 3x+4y=12 ; -4x+3y=-1