In Plane geometry, The parallel line of a line is they have the same slope, so they don't intersect or touch at any point.
To the Line: ax + by = c, the parallel line through Point: (x1,y1)
Parallel Line: Y = (-a/b)X + (a/b)x1 + y1
For example: Line,5X + 2Y = 1, the parallel line through Point(2 , 3), The parallel line slope is -2.5, so the result is Y = -2.5X +8.