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This video is going to be about finding the slopes of horizontal and vertical
lines.
So let's get started.
Here's a graph with a
graph with a horizontal line,
and it looks like it goes through the point... let's see, this looks like a 3,
so that would be
the point
(0, 3).
And we have to find the slope for it.
So let's use the equation for slope. Remember,
the equation for slope is m,
m stands for slope,
equals
y sub 2
minus y sub 1
over x sub 2
minus x sub 1.
So we need to points. We've got a point here already, that's (0, 3), and
we'll take this point.
This point looks like it's
at 4,
so this would be
(4, 3).
And we could call this
x sub 1 and y sub 1,
x sub 2
and y sub 2,
and we'll use this
equation to figure out the slope.
So, m
equals... let's see...
y sub 2 is 3
minus
y sub 1 is 3,
and then
x sub 2 is 4
minus
x sub 1
is 0.
So 3 minus 3
is 0,
and 4 minus 0
is 4.
Well
if I have a fraction...
any time the numerator is 0, that means the fractions equals 0.
So that means this slope
is 0,
and I guess this make sense. Let's look at this line.
You know if I had a positive slope,
the positive slope
would be a line that goes up like that.
So all of these would be positive slopes.
If I had a negative slope, it would be a line that goes down.
So in between all of these lines that go down
and all these lines that go up,
there's this line here that doesn't go up or down.
So in between positive numbers and negative numbers
is going to be just 0.
So my slope
is 0.
And another way to think about this would be... we could write the equation for this line.
So let's try... y equals
mx plus b.
My slope is 0, so y equals... remember m is slope... equals 0x plus
and b will be 3,
plus 3.
And I don't have to write 0x, it doesn't do anything, so this equation is just going to be
y equals 3,
and that makes sense because, looking at this line,
everywhere on this line
the y equals 3.
So if you have a horizontal line, the things to remember...
The slope of a horizontal line
is 0.
The equation for the horizontal line
will be
y equals and then, what number that y always is, and you can just
look at the y-intercept to find out what that number is.
In this case it's 3.
Okay,
let's go on to vertical lines.
Here I've got a vertical line.
It looks like it goes through the point
negative 2, so
that's going to be (-2, 0)
and we'll do the same thing.
So we want to find the slope.
The slope is
y sub 2 minus y sub 1
over x sub 2
minus x sub 1.
I can call this
x sub 1 and y sub 1. I'll take another point, like here,
and that looks like it's at the 3,
so this point
would be... I'm still at negative 2...
(-2, 3).
And we'll call this
x sub 2
and y sub 2.
So let's put these numbers into the equation for the slope.
The slope is going to equal... y sub 2 is 3,
y sub 1 is 0... 3 minus 0
over
negative 2
minus
negative 2 again.
So if we work this out,
we're going to get the slope equals... 3 minus 0 is 3.
Negative 2 minus negative 2.
Two negatives are a positive.
So negative 2 plus 2
will just be 0.
But, remember, I can't divide by 0.
This number in math... any fraction with 0 in the denominator
is undefined.
So that means my slope
for of vertical line
is going to be
undefined,
there's no definition for it,
and we can think of this in terms of an equations, if we want to.
In this case
the x is always negative 2.
So the equation for a vertical line is going to start with x
equals
and then
whatever number the x, this line,
always is. And this line is always at negative 2, all along here.
So I'll have x equals negative 2.
So just to review this one more time...
when you have a horizontal line,
the slope will always be 0
and the equation
will be y equals
whatever number
the line,
whatever y-value the line always is.
For a vertical line,
the slope will always be undefined
and the equation is going to be x
equals
and then whatever x-value
this line always is.
So make sure you understand these.
They occur very often on tests.
Take care, I'll see you next time.