For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal.
Option A:
[tex]y = -2x + 3\\y = 2x-3[/tex]
The slopes are not the same.
Option B:
[tex]y = 2x-1\\y = 2x + 8[/tex]
The slopes are the same so the lines are parallel.
Option C:
[tex]y = 4x + 6\\y = -4x-6[/tex]
The slopes are not the same.
Option D:
[tex]y = -3x + 1\\y = -4x + x-1 = -3x-1[/tex]
The slopes are the same so the lines are parallel.
Answer:
The parallel lines are: Option B and Option D
