Final answer:
The answer to the problem is option D. y = -x + 1, which is the equation of the line that is perpendicular to y = x + 6 and passes through the point (2, -3).
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to another line and passes through a given point. The given line is y = x + 6, which has a slope of 1. To be perpendicular, the slope of the new line must be the negative reciprocal of 1, which is -1. Hence, the slope of the new line is -1.
Now the equation of the line can be written using the point-slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, here (2, -3). The equation becomes y - (-3) = -1(x - 2). Simplifying this we get y = -x + 1.
Therefore, the correct answer is D. y = -x + 1, which is the equation of a line that is perpendicular to y = x + 6 and passes through the point (2, -3).