Final answer:
The slope of any line perpendicular to y = -6 - x is 1. This is found by taking the negative reciprocal of the original slope, which is -1.
Step-by-step explanation:
The slope of any line perpendicular to y = -6 - x is determined by the negative reciprocal of the slope of the given line. The equation y = -6 - x can be rewritten as y = -1x - 6, showing that the slope (m) of this line is -1. To find the slope of a line that is perpendicular to this one, we take the negative reciprocal of -1, which is 1.
Therefore, the slope of the perpendicular line to y = -6 - x is 1. A perpendicular line will have a slope that makes the product of the slopes of the two lines -1. In other words, if we multiply the slope of the given line by the slope of the line perpendicular to it, the result should be -1.