Final answer:
The equation of the line perpendicular to y = x - 1 and passing through the point (-6,2) is y = -x - 4.
Step-by-step explanation:
To find the equation of the line perpendicular to y = x - 1 and passing through the point (-6,2), we need to determine the slope of the given line first. The slope-intercept form of a line equation is y = mx + b, where m represents the slope. Since the given line has a slope of 1, the perpendicular line will have a negative reciprocal slope of -1. Therefore, the slope of the perpendicular line is -1.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we have y - 2 = -1(x + 6). Simplifying, we get y - 2 = -x - 6. Rearranging the equation, we get y = -x - 4. Therefore, the equation of the line perpendicular to y = x - 1 and passing through the point (-6,2) is y = -x - 4.