We are given the equation of the line $3x - 3y = 18$, and we need to find the slope of a line perpendicular to it.

Step 1: Rewrite the equation in slope-intercept form ($y = mx + b$), where $m$ is the slope.

We start with the given equation:

$3x - 3y = 18$

Solve for $y$:

1. Subtract $3x$ from both sides: $-3y = -3x + 18$
2. Divide the entire equation by $-3$ to isolate $y$: $y = x - 6$

The slope of the given line is the coefficient of $x$, which is $m = 1$.

Step 2: Find the slope of the perpendicular line.

The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the slope of the original line is $1$, the negative reciprocal of $1$ is $-1$.

Thus, the slope of the line perpendicular to the given line is:

$\boxed{-1}$

Would you like a deeper explanation, or have any questions?

Here are some related questions to expand your understanding:

1. What is the slope of a line parallel to $3x - 3y = 18$?
2. How do you convert an equation into slope-intercept form in general?
3. What is the geometric meaning of perpendicular slopes?
4. Can the slope of a line be zero, and what does that represent?
5. How do you find the slope of a vertical line?

Tip: The product of the slopes of two perpendicular lines is always $-1$.