Parallel 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.

Problem 1
Are the two lines pictured below parallel?

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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 $$ - \frac{1}{3} $$
Problem 2
Are the two lines below parallel?

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

Perpendicular Lines in Greater Depth
Perpendicular lines:

intersect at $$ 90^{\circ} $$
have slopes that are negative reciprocals
Problem 3
Are the two lines in the picture below perpendicular?

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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 so the lines are perpendicular.

Problem 4
Determine whether or not lines 6 and 5 perpendicular?

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Problem 5
Are line P and line L perpendicular?

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