Set 9: Linear Functions

Explanation

Answer: A

Two lines have slopes $m_1 = a$ and $m_2 = 1/a$ . Are they perpendicular?

No, unless $a = -1$ or $a = 1$ (with sign change)

✓ Correct

Yes, always

No, never

Only if $a = 0$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check product rule. 1. Product: $a \times (1/a) = 1$ . 2. Condition: Perpendicular lines must have a product of $-1$ . 3. Conclusion: They are reciprocals, but not negative reciprocals. So generally No. Strategic Tip: Don't forget the negative sign! $m$ and $-1/m$ are perpendicular. Choice B is incorrect because product is 1. Choice C is incorrect because they could be if $a$ involves complex numbers (out of scope) or specific sign errors in setup. Choice D is incorrect because undefined.

Key Steps:

•

The correct answer is No, unless $a = -1$ or $a = 1$ (with sign change)

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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Set 9: Linear Functions

Detailed Explanation

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