The equation of the line given is:

$3x - 3y = 18$

To find the slope of a line perpendicular to this line, we need to first express the given line in slope-intercept form, which is $y = mx + b$, where $m$ is the slope.

Step 1: Simplify the Equation

We start by simplifying the equation:

$3x - 3y = 18$

Divide the entire equation by 3:

$x - y = 6$

Now, solve for $y$:

$y = x - 6$

So, the equation in slope-intercept form is:

$y = 1x - 6$

Here, the slope $m$ of the line is $1$.

Step 2: Find the Perpendicular Slope

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the original line. The slope of the original line is $1$, so the slope of the perpendicular line is:

$m_{\text{perpendicular}} = -\frac{1}{1} = -1$

Thus, the slope of the line perpendicular to the given line is $-1$.

Would you like any further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How do you find the slope of a line from two points?
2. What is the slope-intercept form of a line?
3. How do you determine if two lines are parallel or perpendicular?
4. What is the equation of a line that passes through a specific point and has a given slope?
5. How does the slope of a line relate to its steepness?

Tip: When dealing with perpendicular slopes, remember that their product is always $-1$.