Question

Which of the following represents an equation of a line perpendicular to the line described by y−2=2x+8 and passes through the point (-1, 12)?

a) y = -1/2 x + 11
b) y = 2 x + 10
c) y = − 2 x + 10
d) y = 1/2 x + 11

Answer 1

The line perpendicular to y - 2 = 2x + 8 that passes through (-1, 12) is y = -1/2 x + 11, which is option (a).

Step-by-step explanation:

The original equation of the line is y - 2 = 2x + 8. To find a line perpendicular to this, we must use the negative reciprocal of the original line's slope. The slope of the given line is 2, so the perpendicular slope will be -1/2. Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we plug in (-1, 12) and our slope to get y - 12 = -1/2(x + 1). Simplifying, we get y = -1/2 x + 11, which corresponds to choice (a).