Final answer:
The slope of a line parallel to the line given by the equation x + y = -6 is -1 since parallel lines have identical slopes.
Step-by-step explanation:
To find the slope of a line parallel to the line whose equation is x + y = -6, first, we need to write the equation in slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept. We can rearrange the given equation to get y = -x - 6. This shows that the slope m of the original line is -1. Lines that are parallel have the same slope, so a line parallel to the original line would also have a slope of -1.