To find the equation of the line that is parallel to the given line $3y - x = -12$ and passes through the point $(18, 2)$, we need to follow these steps:

1. Determine the slope of the given line: Rewrite $3y - x = -12$ in slope-intercept form $y = mx + b$, where $m$ is the slope.

   $3y = x - 12$ $y = \frac{1}{3}x - 4$

   Thus, the slope $m$ of the given line is $\frac{1}{3}$.

2. Find the slope of the parallel line: Since parallel lines have the same slope, the slope of our line will also be $\frac{1}{3}$.

3. Use the point-slope form of a line: With the slope $m = \frac{1}{3}$ and the point $(18, 2)$, we can use the point-slope form $y - y_1 = m(x - x_1)$:

   $y - 2 = \frac{1}{3}(x - 18)$

4. Simplify the equation:

   $y - 2 = \frac{1}{3}x - 6$ $y = \frac{1}{3}x - 4$

So, the equation of the line that passes through $(18, 2)$ and is parallel to $3y - x = -12$ is:

$y = \frac{1}{3}x - 4$

Do you want more details on any step?

Here are five related questions for further exploration:

1. How would you find a line perpendicular to $3y - x = -12$ that passes through $(18, 2)$?
2. What is the significance of parallel and perpendicular slopes?
3. How do you convert from standard form to slope-intercept form?
4. Can you determine the y-intercept from the point-slope form directly?
5. What are the steps to graph a line given in slope-intercept form?

Tip: When two lines are parallel, their slopes are always equal.