Final answer:
The correct line that is perpendicular to the original line y = -(3/5)x + 1 is Option C, which can be rearranged to y = -5/3x + 7, having a slope of 5/3, the negative reciprocal of the original slope -3/5.
Step-by-step explanation:
The question asks which of the following lines is perpendicular to the line y = -(3/5)x + 1. To determine this, we need to find a line that has a slope that is the negative reciprocal of the original line's slope. Since the original line's slope is -3/5, the slope of the line that is perpendicular to it should be 5/3.
Option A, 3x + 5y = 10, can be rearranged to y = -3/5x + 2, which has the same slope as the original line, so it can't be perpendicular. Option B, 3x - 5y = 20, rearranges to y = 3/5x - 4, which also has the wrong slope. Option C, 5x + 3y = 21, can be rearranged to y = -5/3x + 7, and this slope, -5/3, is indeed the negative reciprocal of -3/5. Hence, Option C is the correct answer. Option D, 5x - 3y = 27, rearranges to y = 5/3x - 9, which actually has the exact slope we are looking for, but as the positive reciprocal, hence it is not perpendicular either.