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In the xy-plane, which of the following is the equation of a line that passes through the origin and is perpendicular to the line y=2x+3?

  1. y=-1/2x

  2. y=1/2x

  3. y=2x-3

  4. y=-2x+3

The correct answer is: y=1/2x

A does not pass through the origin. C and D are parallel to y=2x+3 and therefore cannot be perpendicular to it. B is the only option that passes through the origin and has a slope of -1/2, making it perpendicular to the line y=2x+3 which has a slope of 2. The negative reciprocal of 2 is -1/2.