Write an equation of the line that passes through $(6,4)$ and is parallel to the line $3 y-x=-12$.

Step 1 ：Understand the problem: We are asked to find the equation of a line that passes through the point (6,4) and is parallel to the line 3y - x = -12.

Step 2 ：Recall the properties of parallel lines: Parallel lines have the same slope. Therefore, the line we are looking for will have the same slope as the given line.

Step 3 ：Find the slope of the given line: The given line is 3y - x = -12. We can rewrite this as y = 1/3x - 4. Therefore, the slope of the given line is 1/3.

Step 4 ：Use the point-slope form to write the equation of the line: The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (6,4) and has a slope of 1/3. Substituting these values into the point-slope form gives us: \(y - 4 = 1/3(x - 6)\)

Step 5 ：Simplify the equation: To simplify the equation, we distribute the 1/3 on the right side: \(y - 4 = 1/3x - 2\). Then, we add 4 to both sides to isolate y: \(y = 1/3x + 2\)

Step 6 ：Check the solution: Our line is \(y = 1/3x + 2\). This line has the same slope as the given line (1/3), and if we substitute x = 6 into the equation, we get y = 4, which means the line passes through the point (6,4). Therefore, our solution meets the requirements of the problem.

Step 7 ：The equation of the line that passes through the point (6,4) and is parallel to the line 3y - x = -12 is \(\boxed{y = 1/3x + 2}\)