8
algebra

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

A

x=1x = 1

B

y=1y = 1

C

y=3y = 3

D

x=3x = 3

Correct Answer: A

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 becauseyy values change. Choice C is incorrect because it only fits one point. Choice D is incorrect because x is 1, not 3.