identify an equation in point-slope form for the line perpendicular to y=-1/2x+11 that passes through (4,-8). A. y+8=2(x-4)B. y+8+1/2(x-4)C.y-8=1/2(x+4)D.y-4=2(x+8)

Answer:A. y+8=2(x-4)Step-by-step explanation:A line perpendicular to y=-1/2x+11 would have slope +2, which is the negative reciprocal of -1/2.Starting with the slope-intercept form of the equation of a straight line, find the y-intercept based upon this new line's passing through (4, -8):y = mx + b becomes  -8 = 2(4) + b.  Then b = -16, and the desired new line isy = 2x - 16.  Eliminate answer choices B and C, because 1/2 is not the correct slope.Choice A is correct.  Note that the result of subbing 4 for x and -8 for y into A:  y + 8 = 2(x - 4) is a true equation:  -8 + 8 = 2(4 - 4)Also note that y + 8 = 2(x - 4) can be written in slope-intercept form:y = -8 + 2x - 8, or y = 2x - 16 (same as obtained earlier)