Final answer:
To find the equation of a line parallel to another line, use the same slope. The equation of the line is y = (1/6)x - (1/6).
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to determine the slope of the given line.
The equation x - 6y = 48 can be rearranged to y = (1/6)x - 8. This means the slope of the given line is 1/6.
Since the line we want is parallel, it will have the same slope. Using the point-slope form of an equation, we can find the equation of the line that passes through (6, 4) and has a slope of 1/6.
The equation will be y - 4 = (1/6)(x - 6), which simplifies to y = (1/6)x - (1/6).