Final answer:
The equation of the line perpendicular to y-4=-(x-6) and passing through (-2,-2) is y = x - 1, which is option d.
Step-by-step explanation:
The question is asking to find the equation of the line perpendicular to the given line y-4=-(x-6) and that passes through the point (-2,-2). Initially, we should find the slope of the given line. Rewriting the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we have y = -x + 10. This indicates that the slope of the given line is -1. The slope of a line perpendicular to this line would be the negative reciprocal of -1, which is 1. Now, using the point-slope form of the equation (y - y1 = m(x - x1)), where (x1, y1) is the point (-2, -2) and m is the slope 1, we get y - (-2) = 1(x - (-2)) or y + 2 = x + 2. Simplifying this equation to slope-intercept form gives us y = x - 1.