| Start | in this module we're going to learn how
to find the slope of the line this is
something that you all learned a long
time ago but some of your little rust
go over it again
so first of all what is the slope of a line
those are XY axes slope of line is
measured by as they call it the rise
over the run which is another way of
saying every time I go out this much I
go up that much so if I go out this
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| 0:31 | much again I should go out that much
again and of course the line does that
so slope of a line is basically
a way of measuring how fast it's going
up for how slowly it's going up so every
time I go to the right certain unit and
go up certain amount number of units so
in practicality how do we measure that
well im gonna erase these so we can redraw
it
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| 1:02 | that's our line if I want to know how
far I'm going out
that's my change in my x coordinates so
to find this distance I just take the
difference between x1 x2 either way it
doesn't really matter which when you
subtract as long as you're consistent
because you want to get the sin right
know this that this distance will be y1
minus y2 and then I went to ratio so I
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| 1:37 | want to know how much does y go from
y1 to y2 when X goes from x 1 to x 2 for
or as I said you could do it in here the work
y2 minus y1 over x2 minus x1 it doesn't
really matter as long as you're
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| 2:00 | consistent so for example suppose I have a
line that goes through two points 5 12
8,20 going slope but we abbreviate with
the letter M but we indicate the letter m
and is the difference in the y's over
the difference in the X's and as I said
it doesn't matter which order is as long a
your consistent so the right 1 minus the
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| 2:32 | left one the right one minus the left
one and that's the third that means is
every time you got three units to the
right you go up eight units or if you go
one unit to the right you go up eight/thrid units
ok it's very straightforward now
slope as a couple of things we need to
make sure we are aware of when you go this
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| 3:00 | and we do slope we're going to get a
positive number positive so how do we
know well the difference between this X
this X positive number will be a bigger
number minus the smaller number and that
will correspond to a bigger y minus the
smaller y if I'm going down on the
other hand you get a negative slope
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| 3:33 | because now
yeah
because now when i take x1 and subtract x2 i get a positive number but if i
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| 4:05 | take the matching y1 i subtract Y2
which is bigger we are going to get a negative
number
let's use that means to see so suppose
that's three and that's 10 and this is
the point 3 comma 20 and this is the
point 10 comma six then x1 minus x2 im sorry y1
minus y2 over x1 minus x2 will be 10-6
no it's not
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| 4:40 | 20-6 6-20 over 10-3 so y1 is 16 y 2 is 20
x 1 is 10 x2 is 3 so its negative 14 / 7 or
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| 5:00 | negative 2 so that's how you get a
negative slope
what about a horizontal line like this
well notice y1 and y2 is the same
when I have y1 minus y2 one top that's y
minus x to the bottom y1 minus y2 is
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| 5:33 | just going to be 0 because y1 and y2 are the same thing x1 and x2
are going to be different so I'm gonna
get 0ver numbers this is going to come
out 0 so this is zero slope for example
suppose that's three that's ten that's
the point 3 comma 8 and that's point 10
comma 8 the slope will be 8-8
over 10 minus 3 which is 0 in this last kind of
slope
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| 6:08 | what about a vertical line well now i'm
going to zero probably the other
direction so i have a vertical line and
here the X's are the same at the ys are
different so let's say that's the point
3 comma 5 and that's the points 3,10
then y1 minus y2 over x1
minus x2 is 10 minus 5 over 3 minus
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| 6:41 | three which is 5/0, 5/0 it's kinda
weird right
that's zero that's undefined so we say
that this kind of line has no slope or
we could say has an infinite slope
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| 7:03 | and you understand that more when you do
calculus so slope is family by change by
taking the difference the coordinates
now if you have an equation of the line
you can find the slope from the equation
of the line lines can be in the form of
this way you'll see this most often in
calculus work sometimes like this which
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| 7:36 | you saw more often for calculus either
way this is the slope so if you have a
line y equals 2x plus 7 slope is too if
you have this equation y minus 4 is 3
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| 8:00 | times X plus 1 the slope is 3 and
remember this can easily be put into
this point that's all you need to know
that slopes
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