Final answer:
The equation of the line perpendicular to the given line and passing through (−5,3) has a slope of -3 and is derived using the point-slope form. However, there's an inconsistency as none of the provided options match the resulting equation of y = -3x - 12.
Step-by-step explanation:
The question asks for the equation of a line that is perpendicular to the given line with a slope of 1/3 and that passes through the point (−5,3). Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the required line must be −3 (the negative reciprocal of 1/3).
To find the equation of the line, we use the point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in the values, we get: y - 3 = -3(x + 5), simplifying this gives us: y = -3x - 15 + 3, which further simplifies to: y = -3x - 12. However, we have no option matching this result, indicating a potential error in the options provided or in the understanding of the given line to which the new line should be perpendicular. If this is the case, clarification must be sought.