Which of the following equations is parallel to, but not the same as, the line that passes through the points (2, 1) and (6, -1)?
(1) y = 1/2x - 2
(2) y-1 = -1/2(x - 2)
(3) y + 1 = -1/2(x + 6)
(4) y = 1/2x-1

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  (3) y + 1 = -1/2(x + 6)

Step-by-step explanation:

The slope of the line between the two points can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -1)/(6 -2) = -2/4 = -1/2

Then the point-slope form of the equation of the line through the given points can be written as either of ...

  y -1 = -1/2(x -2)

  y +1 = -1/2(x -6)

We note that only choices (2) and (3) have slopes of -1/2, so are parallel. Choice (2) matches the first equation above, so is the identical line, not one that is parallel.

Choice (3) matches neither of the equations of the line through the given point, so that is the choice of interest.

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step-by-step explanation: