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