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Parallel and Perpendicular Lines - Concept
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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

remember it.

This is a different concept.

Two lines are called perpendicular

if they intersect at

a right angle, their slopes are opposite

sign reciprocals.

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.

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