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Set 16: Linear Functions (Advanced)

Explanation

Answer: A

A line passes through (1,3)(1, 3) and (1,5)(1, -5). What is the equation of the line?

A.

x=1x = 1

✓ Correct
B.

y=1y = 1

C.

y=3y = 3

D.

x=3x = 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check the coordinates. 1. Observe: Both points have an x-coordinate of 1. 2. Conclusion: Since xx is always 1, the equation is x=1x = 1. This is a vertical line. 3. Slope Check: 5311=80\frac{-5 - 3}{1 - 1} = \frac{-8}{0} (Undefined), confirming it's vertical. Strategic Tip: If the x-coordinates are the same, it's x=kx = k. If y-coordinates are the same, it's y=ky = k. Choice B is incorrect because yy values change. Choice C is incorrect because it only fits one point. Choice D is incorrect because x is 1, not 3.

Key Steps:

The correct answer is x=1x = 1

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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