Final answer:
To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1. Using the point-slope form of a line, we can find the equation of the perpendicular line by plugging in the given point and slope.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1.
Using the point-slope form of a line, y - y1 = m(x - x1), we can plug in the values of the given point (-12, 10) and the slope (-1) to find the equation:
y - 10 = -1(x - (-12))
y - 10 = -1(x + 12)
y - 10 = -x - 12
y = -x - 2
Therefore, the equation of the line that is perpendicular to y = x - 2 and passes through the point (-12, 10) is y = -x - 2.