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How To Graph Ordered pairs and algebraic relationships In Four Quadrants
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Feb 19, 2025
Welcome back to our pre Algebra class, in today's section we'll learn how to graph points on a coordinate plane also known as the Cartesian plane after Rene Descartes, he was credited with developing the coordinate plane. We'll also learn in this lesson how to graph algebraic relationships. Chapters: 00:00 Introduction 01:06 How To write an ordered pair 01:47 Working on an example 02:34 How to identify the 4 quadrants on a coordinate system 04:41 How to graph ordered pairs on a coordinate plane 10:04 Working on real world problems/ building a function table
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0:00
[Music]
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so
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basically we're going to talk about
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graphing in four quadrant right thus far
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what we talked about in chapter 1 uh
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five or six was just two quadrant right
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one quadrant I mean where it was all
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positive numbers now we going to
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progress from that we're going to make a
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change and we're going to talk about
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graphing more than just one quadrant
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we're going to talk about four quadrants
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right now if you look at street maps I
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don't know if you guys are interested in
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street maps probably not but if you look
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at the street map like most houses are
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built in using this four quadrant model
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they use the coordinate system and is
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the four quad model because some houses
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are located on the left some on the
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right some on the bottom some on the
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bottom left right so they use this kind
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of quadrant to figure out where your
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house is located so this is how they
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built your GPS and you built everything
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else so that people can locate because
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this is the system that they use this is
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the coordinate system and it has
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basically four quadrant right
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now the first thing you want to learn is
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this how do you write an ordered pair
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right we talk about ordered pair in
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chapter one and we say some what is
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unordered pair what is it again if you
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guys remember it has to do with X and Y
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AIS X and Y right and then somebody gave
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me a good definition we said that
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ordered paer was what a couple right and
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then it was ordered it wasn't random it
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was specific we talked about that right
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so now we're going to graduate from that
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and we're going to talk about
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how uh a point graph on a coordinate
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system has an x coordinate and y
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coordinate I just mentioned it okay so
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now we're going to learn how to write
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them and also graph them okay the first
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thing is this if I was to give you an
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example if I say here write the ordered
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pair that has that names each point J
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for example right J has an x coordinate
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of what pay attention here guys
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4 and then y
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coordinate -3 right so if I was to write
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J what would it be it would
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be and then
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comm3 right so this is how you write a
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point an order pair right we we talked
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about X and Y but the only difference is
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is what the only difference here is that
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now X is negative and Y is also negative
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now we're going to learn how to plot
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that on the coordinate system okay
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now the x- axis which is here and the y
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axis they separate the coordinate system
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into four regions we have four regions
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right 1 2 3 and four these are called
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region this is region one this is region
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two this is Region Three and this is
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region four so these two axis because
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the cross at some point they give you
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four separate regions and these regions
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are important now in region one right
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you'll notice that if I was to plot
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something here both the x coordinate and
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the Y coord will be what both positive
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when I put a plus indicates what
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positive right yes um do we have to
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write the region in the Roman numerals
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you can write I mean preferably is Roman
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numeral but you can just write 1 2 3 4
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but Roman num is probably the
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appropriate notation for it right so
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this is quadrant one quadrant two but if
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if you not use this Roman numeral you
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can use 1 2 3 and four right now in
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region one which is called also Quadrant
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One the x coordinate is positive and the
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y coordinate is Nega positive right
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positive they're both positive here both
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X and Y are par now in region
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two uh this is I put X and Y in region
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two x is negative and Y is
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positive in Region Three
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X is negative and Y is also negative
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wait are you making this up or no I'm
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not making it up this is conventional
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this is standard Oh I thought you were
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making an example no this is
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conventional right in region One X is
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positive and Y is positive in region two
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x is negative and Y is positive in
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Region 3 x is negative and Y is negative
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and region four x is positive and Y is
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negative that's just how it is right so
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each region has a set of uh Signs Now
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I'm going to show you how to graph them
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using this let's let's do some examples
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yes can gra something in my yeah go
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ahead now let me show you an example
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here right and that makes perfect sense
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if you graph it so let's say I wanted to
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graph a b c d and
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e I want to graph these points on the
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set of axis right what what's the x
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coordinate of
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a -2 right and the y coordinate is what
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-4 so all my positive right here so let
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me let me put some kind of uh scale here
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and I'll show you exactly how this going
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to
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work so this is 1 2 3 4 5 6 7 8 1 2 3 4
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5 6 7 8 now if I'm going this on the
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left side is what - 1 2
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-34
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57 if I'm going down is also
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-1 -2
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-34 5 -6
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-78 now here's a
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problem I want to PL -2 and4 right X is
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-2 I'm not going to be on the right or
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the left
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side Left Right X is -2 y is4 so X is -2
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is right here y is4 1 2 3 4 and what do
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I
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do where the intercept is where a is
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going to be located right does that make
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sense to everybody yes or no all right
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so that's a and we can put a here
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because -24 now B is 0 and -2 right B is
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0 and -2 x is 0 Y is -2 I'm not going
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down down or up down down right now let
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me pause for a second let me ask you a
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question what quadrant is a located
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in
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yeah give what quadrant is a
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in three three right a is in
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Q3 or Q3 whichever one you want to use
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right what about B what
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quadrant is B any
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quadrant yes or no yes are you sure no
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right cuz B is on what the Y AIS right
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so it's not on any quadrant cuz now cuz
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it's right here on the line so it's near
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here neither here it's on the line so B
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is in no quadrant does that make sense
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yeah because it's on the line right now
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what about c c x is 3 1 2 3 Y is 1 right
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right
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here so what quadrant is seeing
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what's that Quadrant 4 she's in Quadrant
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4 Q4 right or Quadrant 4 right now what
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about
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d d x is
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1-1 and Y is four 1 2 3
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4 so what quad is d uh
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Vicki what quad is
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which quadrant is
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this these is right
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here quadrant
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two right this is quadrant one this is
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quadrant 2 this is quad 3 and this is
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Quad 4 these here because it's -1 x is1
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y is 4 so this is quadrant to so D is in
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Q2 all right now what about e
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one and five right one and five is right
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here viy what's
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that quadrant one so do you see how we
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graph this point right you you just have
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to make sure you respect the order in
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which these are labeled if it's negative
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it's always X and Y first you always put
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the x coordinate and the y coordinate
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it's not Y and X right X and Y X and Y
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because sometimes what happened is
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people see this and they put -4 -2 no
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it's not the same as -2 and4 you always
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start with the left and then right so X
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first and then Y X and Y X and Y does
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that make sense on the x axis yet
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something that will really help me is
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always label each line right so then I
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always like that's X that's X and that's
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a y that's right you can do that and
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then put here y AIS put a label on it
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and then x axis
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that way you never have any problems
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figuring out what quadrant you're
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supposed to be in does that make sense
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I'll be good on this so now we going to
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work on the word problem real
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quick all right
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so so the sum
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of two golf
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scores is
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three if
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x
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represents one
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score and
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Y represents
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the yeah
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SC make a
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function name five
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presidents any any five president
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no except
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those except those on you have to name
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like Kennedy and stuff no he's too easy
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accept him all right so here's the thing
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so let's read this real quick the sum of
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two gol scores is three right the sum of
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the two scores is three the x if x
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represent one score and Y
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eight pay attention here the sum of the
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two scores is what three right X
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represent one score and Y represent the
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other score
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if that's the case they want you to make
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a function table of possible values for
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x and y and then graph it right let's
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try and see if you can make like five
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values so we know that the sum of the
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two scores is three so how would you
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write that 2 =
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3 right yes x + y = 3 x + y = 3 that is
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the function right x + y = 3 now we need
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to find possible values that can give us
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that right
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so everybody's going to have something
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different this is X and Y and we want to
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figure out what x values and what y
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value can give us to give me some random
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values that can add up to three
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yeah two one two and one right two and
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one two and one what
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else um El three and zero three and zero
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what
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else yeah
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one and two you already said two and one
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you know one and two yeah um 1.5 + 1.5
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uh yeah that's a good one but I want I
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want to stick to like integers for now I
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want you to try and see if you can
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figure out some negatives as well
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yeah3 + 6 thank you -3 + POS 6 that's
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also three another one
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huh think about another one that has a
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negative in it yeah -10 + 13-1 + 13 all
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right right and another one that has a
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negative in
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it four and four and
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what 1 right
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41 right now let's try to PLU those on
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the set of axis right let me try to PLU
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these here and now we going to figure
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out what quadrant they belong in right
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so 2 and one what quad is are going to
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be in two and
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one
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yeah two and one it's going to be in mhm
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three 2 and One X is 2 Y is one positive
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so what's that what Quant is that three
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no one first quadrant X is
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2 Y is 1
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Right Here Right Now the second 3 0 what
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quadrant you sure what 3
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0 yes 3 0 um no Quant no quadrant is on
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where it's right here right three Z is
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on the line so he not in any quadrant
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because he lies on the line does that
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make sense or it's both what about3 and
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6 -3 6 where am I going to put that
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at where is3 oh wait sorry3 right sorry
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and six right here what quadrant is
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this two quadrant two Q2 right I'm here
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and then -10 and 13 is also going to be
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what
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quad -10 and then 13 where am I going to
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L it's also going to be here right this
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is 8 9 10 13 is somewhere here so I'm
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going to proba be somewhere here is
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quadrant what
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Q2 this is the quadrant 2 cuz I'm still
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here right cuz this goes up and this
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goes up it's still and then
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41 no that what's that going to be at 4
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1
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Quant quadrant four four here 1 I'm
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going to be right here this is Q4
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Quadrant 4 all right so this is how you
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use uh this quadrant and then to graph
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the the points or the Ed pairs it's
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really super easy you just have to read
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it over again okay so what to take away
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from this lesson we just need to know
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that now we are graduating
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from one quadrant to like four quadrant
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now we have the negatives and the
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positives and we have a total of four
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regions region one Region 2 Region Three
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and region four and it's always X first
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and a y coordinate x coordinate first
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and qu right and then identify where the
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quadrants are once you plug the point
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anything that lies on the line is not on
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any quad all right so I'm going to give
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you guys some work to do tomorrow and
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then we're going to be going to Mrs
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Hoffman's room that's where you're going
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to be at no homework