Question 162492
x = 5x + 1
I will assume that this is incorrect and what is really being expressed is y=5x+1
.{{{ graph( 300, 200, -10, 10, -10, 10,5x+1, 5x+6) }}} 


In that case it is parallel to y = 5x + 6
because they have the same slope

y = -5x - 6 is neither.{{{ graph( 300, 200, -10, 10, -10, 10,-5x-6, 5x+6) }}} 



x = -5y + 6

This line is perpendicular because the slope is inverse and is -. This is the definition of  a perpendicular line
.{{{ graph( 300, 200, -10, 10, -10, 10,-.2x+6, 5x+6) }}}