WEBVTT
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welcome to our algebra preview focusing on plotting in Cartesian
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coordinates. The reason we're gonna go over this even
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though it may seem fun, amazing, trivial is
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that it is absolutely a wonderful tool for visualizing what's
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happening in physics. So, um, let's get
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started, then. Remember the Cartesian coordinates. That
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means we're using the standard X and Y axes is
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some people sometimes refer to it. Okay. And
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what we're gonna do here is we're gonna always say
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that the X axis, the horizontal axis is our
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independent variable, while the Y axis are vertical,
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axis is going to be our dependent variable. So
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the way we might write that in physics might be
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, for example, V of tea is equal to
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weigh. Might say fee not plus acceleration, times
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time. And we'll talk more about this equation when
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we get into Kim Dramatic section. Um, but
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what this means is that we need to be able
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to look at this and dry on a Cartesian plot
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to really understand what's going on. So let's throw
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on some numbers that might seem a little bit more
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familiar. Say we have, uh, actually,
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let's just say we're gonna do a plot of F
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of X is equal to X. Okay, so
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remember ffx here we're just substituting in for why goes
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on the y Axis X and since it's always equal
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to it at X equals zero f of X equals
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zero at X equals one f of X equals one
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X equals two f x equals two and so on
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and so forth. So what we get is actually
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a straight line a straight as I can draw it
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. Um, that extends in both directions. Okay
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, Um and this is part of a standard set
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of straight lines that we get from an equation that
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generally has written something like this. Why equals m
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x plus b where again we're using. Why on
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our vertical axis? And in this case, we
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have called M Slope and B is referred to as
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the Y intercept the reason for that being and notice
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if X equals zero i e. Here on the
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y axis, then why is equal to be,
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which means that B is the amount at which we
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cross the y axis. So, for example,
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say we have ah function F of X is equal
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to x minus one Okay, so f of X
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versus X. Okay, X minus one. That
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means that X equals zero f of X equals negative
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one. So we're here, then we go over
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one and up one, and we are there,
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so we're going to get in. Fact, this
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line is parallel to the first one I drew.
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It's just shifted down by one. On the other
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hand, if I were toe, multiply it there
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. Say we have a function f of X equals
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two X minus one. Now, when I put
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ffx on my Y axis and X on my X
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axis, then I'm going to still pass through negative
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one X equals zero. But when I move over
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one I'm also going to go up to. So
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I'm gonna end up here, so I'm gonna have
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a line this'll way. So it has an intersection
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point with the previous line I drew over here,
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but it has a different slope, so it's not
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going to run parallel to either of the previous lines
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that I've drawn. Now we could have a more
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complicated situation where instead of just a linear equation,
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we have something like f X equals X squared.
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Now Some of you may remember that immediately what it
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looks like, but just to plug it in.
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Remember, if X equals zero, then ffx would
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be zero here. X equals one. FX will
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be one if X equals negative one. We also
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get one, because negative one squared is one negative
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. Two squared is gonna be 1234 and two squared
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is also gonna be four. And we end up
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with this. Nice what we call parabolic arc that's
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drawn in here. Okay? And we can continue
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and, uh, increase the complexity here. But
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the basic ideas you plug in numbers for the independent
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variable on the right hand side, solve for what
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the dependent variable is. And then plot that in
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terms of your ex. Why coordinates? Or in
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this case, what we're writing is X f of
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X coordinates, and this is how you plot in
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Cartesian coordinates.