Final answer:
The slope of a line perpendicular to 3x - 3y = 63 is -1.
Step-by-step explanation:
To find the slope of a line perpendicular to the line whose equation is 3x - 3y = 63, we need to first find the slope of the given line.
The equation is already in the form of y = mx + b, where m is the slope.
So let's rearrange the equation to isolate y: -3y = -3x + 63.
Dividing both sides by -3 gives us y = x - 21. The slope of this line is 1.
A line perpendicular to another line has a slope that is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to y = x - 21 is -1/1, which simplifies to -1.
Therefore, the slope of a line perpendicular to the line whose equation is 3x - 3y = 63 is -1.