Parallel and Perpendicular Lines - Concept
There are special rules to help us find the equation of a line given an equation of a line that is parallel or perpendicular to it. Parallel and perpendicular lines have related slopes. Parallel lines have equivalent slopes and perpendicular lines have negative inverses of their slopes. To fully understand and apply this concept, we should be familiar with the slope and the slope-intercept form of an equation.
Working with parallel and perpendicular
lines is really important not
only in algebra but also in geometry.
So this is a concept you are
going to want to review at the end of
your algebra course before you move
on to geometry.
First thing, two lines are parallel if they never
cross. Their slopes are the same.
A lot of people think of
railroad tracks when they think about
parallel lines. If in your
brain you picture how railroad ties are
-- is that what they are called?
Ties? I think so. They're always
parallel. They never, ever
cross and they go on forever and ever
across the land. I guess not
forever and ever. That's the idea
of parallel lines.
If you are looking at the equations, you will
know two lines are parallel without
having graphed them if their slopes
are the same. Let me draw a
quick picture of that. Slopes, remember,
means how steep the lines
are. So slopes are the same, means
those two lines are equally steep.
That's something that might help you
This is a different concept.
Two lines are called perpendicular
if they intersect at
a right angle, their slopes are opposite
So let's look at a picture.
This is, again, not perfect,
but picture of two perpendicular
lines. Perpendicular lines means
they cross at a right angle. So
if I draw this line right here, a perpendicular
line would look kind of
like that. That's not great. You
could tell it was perpendicular
if you took your paper and you stuck
it right in the corner there, it
would fit perfectly, all four corners.
Mine isn't great. You get the idea.
Perpendicular lines mean they cross
a right angle which is 90 degrees and
you will work with that a lot in geometry.
Let's talk more about opposite sign reciprocal
slopes. Like, if I gave you the number
-2, the reciprocal of 2 is
1/2. Notice, also, how instead of
-2 I wrote positive 1/2. These
are opposite signs, meaning one's positive,
one's negative and they're
reciprocals. Another example would
be, like, 3/4 and the opposite
sign reciprocal would be -4/3.
These are the kinds of slopes that
we're looking for when we're talking
about perpendicular lines. These
are things you are just going to have
to memorize: Parallel never cross,
same slope; perpendicular means they
cross at a right angle, opposite
sign reciprocals. There's no real
shortcuts to it. But these
are really, really important definitions
that you'll need in algebra and
also in geometry.