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What is an equation of the line that passes through the point (6, 4) and is parallel to the line x - 6y = 48?

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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).

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