Final answer:
The slope of a line perpendicular to the line with equation 2x + 2y = 24 is 1, obtained by finding the negative reciprocal of the original line's slope, which is -1.
Step-by-step explanation:
To find the slope of a line perpendicular to the given line 2x + 2y = 24, we first find the slope of the given line. We rearrange the equation in the slope-intercept form, y = mx + b, where m represents the slope. Starting from 2x + 2y = 24, we subtract 2x from both sides to get 2y = -2x + 24, and then divide by 2 to get y = -x + 12.
Here, the slope of the given line is -1. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to 2x + 2y = 24 is the negative reciprocal of -1, which is 1.