Final answer:
The equation of the line parallel to y = 9 - (x + 10) and goes through the point (-8, 12) is y = -x + 4.
Step-by-step explanation:
The equation of the line that is parallel to y = 9 - (x + 10) and goes through the point (-8, 12) can be found using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the given line is parallel to our desired line, they must have the same slope. The slope of the given line can be found by rearranging it to the slope-intercept form: y = -x - 1. The slope is -1.
Using the point-slope form, we can find the equation of the desired line:
y - y1 = m(x - x1)
y - 12 = -1(x - (-8))
y - 12 = -1(x + 8)
y - 12 = -x - 8
y = -x + 4