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Which equation represents the line that is perpendicular to and passes through (-6,-9)?

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Final answer:

The equation of the line perpendicular to and passing through (-6,-9) is y = (-1/3)x + 7.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line.

The given line has a slope of 3. Therefore, the line perpendicular to it will have a slope of -1/3.

Using the point-slope form, we can write the equation of the line as y - (-9) = (-1/3)(x - (-6)). Simplifying this equation gives us y = (-1/3)x + 7.

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