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On the Khan Academy web app,
which I need to work on a

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little bit more to make it a
little bit faster, they have

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this one module that's called
the graph of the line.

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It has no directions on it, and
I thought I would make a little

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video here, at least to explain
how to do this module, and in

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the process, I think it'll help
people, even those of you who

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aren't using the module,
understand what the slope and

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the y-intercept of a line
is a little bit better.

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So this is a screen shot of
that module right here, and the

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idea is essentially to change
this line, and this line right

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here in orange is the line
specified by this equation

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right here, so right now it's
the equation of the

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line 1x plus 1.

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It has a slope of 1, you can
see that, for every amount it

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moved to the right it moves up
exactly 1, and has 1

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for its y-intercept.

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It intersects the y-axis
at exactly the point 0,1.

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Now, the goal of this exercise
is to change your slope and

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your y-intercept so that you go
through these two points, and

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this point's-- half of it's off
the screen, hopefully you can

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see them if you're watching
these in HD-- you can

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see these two points.

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Our goal is to make this line
go through them by essentially

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changing its equation.

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So it's a kind of a tactile way
of-- you know, as tactile as

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something on the computer can
get-- of trying to figure out

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the equation of the line that
goes through these two points.

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So how can we do that?

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So you can see here, when I
change the slope, if I make

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the slope higher, it
becomes more steep.

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Now the slope is 3.

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For every 1 I move to the
right, I have to go 3 up.

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My change in y is 3 for
every change in x of 1.

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Or that's my slope.

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My y-intercept is still 1.

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If I change my y-intercept, if
I make it go down, notice it

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just shifts the line down.

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It doesn't change its
inclination or its slope, it

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just shifts it down along
this line right there.

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So how do I make my line go
through those two points?

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Well it looks like, if I shift
it up enough-- let's shift up

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that point-- and then let's
say let's lower the slope.

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This looks like it has
a negative slope.

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So if I lower my slope, notice
I'm flattening out the line.

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That's a slope of 0.

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It looks like it has to be
even more negative than that.

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Let's see, maybe even more
negative than that, right?

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It has to look like a line that
goes bam, just down like that.

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Even more-- that looks close.

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Let me get my y-intercept
down to see if I can

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get closer to that.

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It still seems like my slope
is a little bit too high.

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That looks better.

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So let me get my y-intercept
down even further.

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It's now intersecting way
here, off the screen.

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You can't even see that.

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I just realized this is
copyright 2008 Khan

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Academy, it's now 2009.

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It's almost near
the end of 2009.

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I could just change that.

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Maybe I'll just
write 2010 there.

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OK.

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So y-intercept.

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Even more.

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So I lowered the y-intercept
but our slope is still

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not strong enough.

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The y-intercept is
actually off the chart.

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It's intersecting at minus 18.

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That's our current y-intercept.

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But the slope of minus 5
is still not enough, so

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let me lower the slope.

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So if I lower the slope, let's
see, if I lower the y-intercept

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a little bit more,
is that getting me?

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There you go.

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It got me to those points.

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So the equation of the line
that passes through both

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of those things is
minus 6x minus 22.

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Let's do another one.

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So, once again, it resets it,
so I just say the equation 1x

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plus 1, but it gives me these
two new points that I have

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to make it go through.

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And once again this is going to
be a negative slope, because

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for every x that I move
forward positive, my y

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is actually going down.

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So I'm going to have a negative
slope here, so let me lower

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the slope a little bit.

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It's actually doing fractions,
so this thing jumps

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around a little bit.

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I should probably change
that a little bit.

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That looks about right, so let
me shift the graph down a

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little bit by lowering
its y-intercept.

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By lowering its y-intercept,
can I hit those two points?

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There you go.

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This is the equation of that
line that goes to the points

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minus 5,1 and the
points 9,minus 9.

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You have a slope of minus 5/7.

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For every 7 you go to the
right, you go down 5.

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If you go 1, 2, 3, 4, 5,
6, 7, you're going to

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go down 1, 2, 3, 4, 5.

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And that, we definitely
see that on that line.

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And then the y-intercept is
minus 18 over 7, which is a

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little over 2, it's about a
little over-- it's what,

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a little over 2 and 1/2.

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And we see right there
that the y-intercept is

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a little over 2 and 1/2.

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That's the equation
for our line.

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Let's do another one.

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This is a fun module, because
there are no wrong answers.

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You can just keep messing with
it until you eventually get

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that line to go through both of
those points, but the idea is

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really give you that intuition
that the slope is just what the

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inclination of the line is, and
then the y-intercept is how far

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up and down it gets shifted.

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So this is going to be
a positive slope, but

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not as high as 1.

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It looks like, for every 1, 2,
3, 4, 5, 6, 7, 8, 9, 10, 11,

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12, for every 12 we go to the
right, we're going

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to go 1, 2, 3 up.

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So our slope is going to be 3
over 12, which is also 1 over

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4, and we can just look
at that visually.

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Let's lower our slope.

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That's 3/4, not low enough.

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1/2, not low enough.

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1/4, which I just figured out
it is, that looks right, and

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then we have to lower
the y-intercept.

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We're shifting it down,
and there we go.

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So the equation of this line,
its slope is 1/4, so the

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equation of the line
is 1/4x plus 1/4.

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So hopefully, for those of you
trying to do this module, that,

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1, explained how to do it, and
for those of you who don't even

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know what this module is, it
hopefully gives you a little

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intuition about what the slope
and the y-intercept do

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to an actual line.