What is the equation of the line passing through (2,-3) and perpendicular to the line y = 2x + 3?
Correct: A
The slope of the line y = 2x + 3 is 2. The slope of a line perpendicular to this line will be the negative reciprocal of 2, which is -1/2. The equation of the line can be written in point-slope form as y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point on the line. Substituting in m = -1/2, x1 = 2, and y1 = -3, we have y - (-3) = -1/2 (x - 2), which simplifies to y + 3 = -1/2 x + 1. Subtracting 3 from both sides gives y = -1/2 x - 2.