Final answer:
To find the equation of a line parallel to 3y - x = -12 that passes through (18, 2), we determine the slope of the original line, which is 1/3, and use the point-slope form with the given point. The resulting equation is y = (1/3)x - 4.
Step-by-step explanation:
The question is asking to find the equation of a line that is parallel to the given line 3y - x = -12 and passes through the point (18, 2). First, we should find the slope of the given line by rewriting it in slope-intercept form (y = mx + b). The original equation can be rearranged to y = (1/3)x + 4, which shows that the slope (m) is 1/3. Since parallel lines have the same slope, the new line will also have a slope of 1/3.
Now, we can use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting the given point (18, 2) and the slope 1/3, we get y - 2 = (1/3)(x - 18). Finally, we can simplify this to y = (1/3)x - 4 as the equation of the line parallel to 3y - x = -12 that passes through (18, 2).