Consider the line y=3x-1
what is the slope of a line parallel to this line
What is the slope of a line perpendicular to this line?
we know that
If two lines are parallel, then their slopes are equal
so
Part 1) what is the slope of a line parallel to this line
the slope of the given line is m=3
therefore
the slope of the parallel line is m=3
Part 2)
If two lines are perpendicular, then their slopes are opposite reciprocal
therefore
the slope of the perpendicular line is m=-1/3