Final answer:
The slope of a line perpendicular to the line with the equation 3x – 3y = 54, after solving for y and finding the original slope as 1, is -1, which is the negative reciprocal of 1.
Step-by-step explanation:
The slope of a line perpendicular to a given line can be found by taking the negative reciprocal of the slope of the given line. First, we need to find the slope of the original line, which is given by the equation 3x – 3y = 54. To express this equation in slope-intercept form (y = mx + b), we solve for y to get y = x - 18, where the slope (m) is 1. The slope of the perpendicular line would then be the negative reciprocal of 1, which is -1.