Question

How do i find the slope of a line that passes through a given point and is parallel or perpendicular to another given point?

Answer 1

There's no such thing as parallel or perpendicular "to a point".  A problem like that
will always want the new line to be parallel or perpendicular to another line.

-- If the new line is parallel to the given line, then they have the same slope.

-- If the new line is perpendicular to the the given line, then the slope of the
new line is [ 1 / slope of the given line ].

In either case, you now have the slope of the new line and a point on it. 
From there, you should have no trouble finding its equation.

Answer 2

Parallel is same slope.
Perpendicular is same slope but you have make it opposite and flip it.
For example if your slope is 2/3. For Perpendicular it would be - 3/2.