Parallel lines have the same slope, while perpendicular lines have an opposite reciprocal slope.
Line 1:
-5y = 3x + 7
y = -3/5x - 7/5
Line 2:
y = -5/3x + 8
Line 3:
6x - 10y = -4
-10y = -6x - 4
y = 3/5x + 2/5
Line 1 and Line 2 are neither perpendicular nor parallel. While their slopes are reciprocals of each other, the signs are not opposite (both are negative).
Line 1 and Line 3 are neither perpendicular nor parallel. While the slope itself is the same, the signs are different.
Line 2 and Line 3 are perpendicular. Their slopes are opposite reciprocals of each other.
Hope this helps!! :)