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.