Parallel and Perpendicular Lines

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).
Parallel Lines in greater depth

On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of  these lines intersects at 90 degrees.
Perpendicular Lines in greater depth.

Both of the lines below have the same slope: $$ \frac{1}{2} $$
Therefore these lines are parallel and will never meet.

Are the two lines pictured below parallel?

Answer

No

While these lines may look parallel at first glance, if you look closely and calculate each line's slope, you will find that:

line 1 has a slope of $$ -\frac{1}{4} $$
line 2 's slope is  $$ - \frac{1}{3} $$.

Are the two lines below parallel?

Answer

Yes these lines have the same slope, 2, and clearly are never going to intersect.

Are the two lines in the picture below perpendicular?

Answer

Yes.
The slope of line 1 is -2 and
that of line 2 is$$ \frac{1}{2}$$. -2 and$$ \frac{1}{2}$$  are negative reciprocals.

Determine whether or not lines 6 and 5 perpendicular?

Answer

Yes.
Line 5 's slope is$$ \frac{3}{2}$$ 2 and line 6 's is$$ -\frac{2}{3}$$ , which are negative reciprocals.

Are Line P and line L perpendicular?

Answer

They are not perpendicular because their slopes are not negative reciprocals of one another.