Final answer:
The equation of the line perpendicular to y = -x - 3 and passing through (6, 5) is y = x - 1. The equation of the line parallel to y = -x - 3 and passing through (6, 5) is y = -x + 11.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -x - 3, we first determine the slope of the given line, which is -1. The slope of any line perpendicular to this would be the negative reciprocal, which is 1. Using the point (6, 5) and the slope 1, we use the point-slope form to find the equation of the perpendicular line: y - 5 = 1(x - 6), simplifying to y = x - 1.
For the parallel line, we require a line with the same slope as the given line, which is -1. Using the point (6, 5) again, we write the point-slope form: y - 5 = -1(x - 6), simplifying to y = -x + 11 for the equation of the line parallel to the given line.