[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.72,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.72,0:00:03.54,Default,,0000,0000,0000,,On the Khan Academy web app,\Nwhich I need to work on a
Dialogue: 0,0:00:03.54,0:00:05.57,Default,,0000,0000,0000,,little bit more to make it a\Nlittle bit faster, they have
Dialogue: 0,0:00:05.57,0:00:08.59,Default,,0000,0000,0000,,this one module that's called\Nthe graph of the line.
Dialogue: 0,0:00:08.59,0:00:11.69,Default,,0000,0000,0000,,It has no directions on it, and\NI thought I would make a little
Dialogue: 0,0:00:11.69,0:00:14.80,Default,,0000,0000,0000,,video here, at least to explain\Nhow to do this module, and in
Dialogue: 0,0:00:14.80,0:00:17.87,Default,,0000,0000,0000,,the process, I think it'll help\Npeople, even those of you who
Dialogue: 0,0:00:17.87,0:00:21.82,Default,,0000,0000,0000,,aren't using the module,\Nunderstand what the slope and
Dialogue: 0,0:00:21.82,0:00:24.59,Default,,0000,0000,0000,,the y-intercept of a line\Nis a little bit better.
Dialogue: 0,0:00:24.59,0:00:27.38,Default,,0000,0000,0000,,So this is a screen shot of\Nthat module right here, and the
Dialogue: 0,0:00:27.38,0:00:31.55,Default,,0000,0000,0000,,idea is essentially to change\Nthis line, and this line right
Dialogue: 0,0:00:31.55,0:00:34.64,Default,,0000,0000,0000,,here in orange is the line\Nspecified by this equation
Dialogue: 0,0:00:34.64,0:00:36.84,Default,,0000,0000,0000,,right here, so right now it's\Nthe equation of the
Dialogue: 0,0:00:36.84,0:00:38.51,Default,,0000,0000,0000,,line 1x plus 1.
Dialogue: 0,0:00:38.51,0:00:42.45,Default,,0000,0000,0000,,It has a slope of 1, you can\Nsee that, for every amount it
Dialogue: 0,0:00:42.45,0:00:46.21,Default,,0000,0000,0000,,moved to the right it moves up\Nexactly 1, and has 1
Dialogue: 0,0:00:46.21,0:00:47.62,Default,,0000,0000,0000,,for its y-intercept.
Dialogue: 0,0:00:47.62,0:00:52.13,Default,,0000,0000,0000,,It intersects the y-axis\Nat exactly the point 0,1.
Dialogue: 0,0:00:52.13,0:00:55.92,Default,,0000,0000,0000,,Now, the goal of this exercise\Nis to change your slope and
Dialogue: 0,0:00:55.92,0:00:59.41,Default,,0000,0000,0000,,your y-intercept so that you go\Nthrough these two points, and
Dialogue: 0,0:00:59.41,0:01:02.30,Default,,0000,0000,0000,,this point's-- half of it's off\Nthe screen, hopefully you can
Dialogue: 0,0:01:02.30,0:01:04.94,Default,,0000,0000,0000,,see them if you're watching\Nthese in HD-- you can
Dialogue: 0,0:01:04.94,0:01:06.73,Default,,0000,0000,0000,,see these two points.
Dialogue: 0,0:01:06.73,0:01:10.70,Default,,0000,0000,0000,,Our goal is to make this line\Ngo through them by essentially
Dialogue: 0,0:01:10.70,0:01:12.21,Default,,0000,0000,0000,,changing its equation.
Dialogue: 0,0:01:12.21,0:01:18.11,Default,,0000,0000,0000,,So it's a kind of a tactile way\Nof-- you know, as tactile as
Dialogue: 0,0:01:18.11,0:01:21.01,Default,,0000,0000,0000,,something on the computer can\Nget-- of trying to figure out
Dialogue: 0,0:01:21.01,0:01:23.56,Default,,0000,0000,0000,,the equation of the line that\Ngoes through these two points.
Dialogue: 0,0:01:23.56,0:01:24.89,Default,,0000,0000,0000,,So how can we do that?
Dialogue: 0,0:01:24.89,0:01:27.65,Default,,0000,0000,0000,,So you can see here, when I\Nchange the slope, if I make
Dialogue: 0,0:01:27.65,0:01:30.27,Default,,0000,0000,0000,,the slope higher, it\Nbecomes more steep.
Dialogue: 0,0:01:30.27,0:01:31.41,Default,,0000,0000,0000,,Now the slope is 3.
Dialogue: 0,0:01:31.41,0:01:35.09,Default,,0000,0000,0000,,For every 1 I move to the\Nright, I have to go 3 up.
Dialogue: 0,0:01:35.09,0:01:38.21,Default,,0000,0000,0000,,My change in y is 3 for\Nevery change in x of 1.
Dialogue: 0,0:01:38.21,0:01:39.47,Default,,0000,0000,0000,,Or that's my slope.
Dialogue: 0,0:01:39.47,0:01:41.13,Default,,0000,0000,0000,,My y-intercept is still 1.
Dialogue: 0,0:01:41.13,0:01:44.26,Default,,0000,0000,0000,,If I change my y-intercept, if\NI make it go down, notice it
Dialogue: 0,0:01:44.26,0:01:45.92,Default,,0000,0000,0000,,just shifts the line down.
Dialogue: 0,0:01:45.92,0:01:48.18,Default,,0000,0000,0000,,It doesn't change its\Ninclination or its slope, it
Dialogue: 0,0:01:48.18,0:01:50.72,Default,,0000,0000,0000,,just shifts it down along\Nthis line right there.
Dialogue: 0,0:01:50.72,0:01:54.85,Default,,0000,0000,0000,,So how do I make my line go\Nthrough those two points?
Dialogue: 0,0:01:54.85,0:01:58.89,Default,,0000,0000,0000,,Well it looks like, if I shift\Nit up enough-- let's shift up
Dialogue: 0,0:01:58.89,0:02:01.21,Default,,0000,0000,0000,,that point-- and then let's\Nsay let's lower the slope.
Dialogue: 0,0:02:01.21,0:02:03.05,Default,,0000,0000,0000,,This looks like it has\Na negative slope.
Dialogue: 0,0:02:03.05,0:02:07.13,Default,,0000,0000,0000,,So if I lower my slope, notice\NI'm flattening out the line.
Dialogue: 0,0:02:07.13,0:02:08.88,Default,,0000,0000,0000,,That's a slope of 0.
Dialogue: 0,0:02:08.88,0:02:11.48,Default,,0000,0000,0000,,It looks like it has to be\Neven more negative than that.
Dialogue: 0,0:02:11.48,0:02:14.20,Default,,0000,0000,0000,,Let's see, maybe even more\Nnegative than that, right?
Dialogue: 0,0:02:14.20,0:02:17.36,Default,,0000,0000,0000,,It has to look like a line that\Ngoes bam, just down like that.
Dialogue: 0,0:02:17.36,0:02:19.75,Default,,0000,0000,0000,,Even more-- that looks close.
Dialogue: 0,0:02:19.75,0:02:22.81,Default,,0000,0000,0000,,Let me get my y-intercept\Ndown to see if I can
Dialogue: 0,0:02:22.81,0:02:26.11,Default,,0000,0000,0000,,get closer to that.
Dialogue: 0,0:02:26.11,0:02:28.94,Default,,0000,0000,0000,,It still seems like my slope\Nis a little bit too high.
Dialogue: 0,0:02:28.94,0:02:29.87,Default,,0000,0000,0000,,That looks better.
Dialogue: 0,0:02:29.87,0:02:32.95,Default,,0000,0000,0000,,So let me get my y-intercept\Ndown even further.
Dialogue: 0,0:02:32.95,0:02:35.00,Default,,0000,0000,0000,,It's now intersecting way\Nhere, off the screen.
Dialogue: 0,0:02:35.00,0:02:37.05,Default,,0000,0000,0000,,You can't even see that.
Dialogue: 0,0:02:37.05,0:02:39.48,Default,,0000,0000,0000,,I just realized this is\Ncopyright 2008 Khan
Dialogue: 0,0:02:39.48,0:02:41.10,Default,,0000,0000,0000,,Academy, it's now 2009.
Dialogue: 0,0:02:41.10,0:02:42.31,Default,,0000,0000,0000,,It's almost near\Nthe end of 2009.
Dialogue: 0,0:02:42.31,0:02:43.68,Default,,0000,0000,0000,,I could just change that.
Dialogue: 0,0:02:43.68,0:02:45.47,Default,,0000,0000,0000,,Maybe I'll just\Nwrite 2010 there.
Dialogue: 0,0:02:45.47,0:02:45.84,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:02:45.84,0:02:47.28,Default,,0000,0000,0000,,So y-intercept.
Dialogue: 0,0:02:47.28,0:02:49.94,Default,,0000,0000,0000,,Even more.
Dialogue: 0,0:02:49.94,0:02:52.21,Default,,0000,0000,0000,,So I lowered the y-intercept\Nbut our slope is still
Dialogue: 0,0:02:52.21,0:02:53.08,Default,,0000,0000,0000,,not strong enough.
Dialogue: 0,0:02:53.08,0:02:54.87,Default,,0000,0000,0000,,The y-intercept is\Nactually off the chart.
Dialogue: 0,0:02:54.87,0:02:57.20,Default,,0000,0000,0000,,It's intersecting at minus 18.
Dialogue: 0,0:02:57.20,0:02:58.45,Default,,0000,0000,0000,,That's our current y-intercept.
Dialogue: 0,0:02:58.45,0:03:00.73,Default,,0000,0000,0000,,But the slope of minus 5\Nis still not enough, so
Dialogue: 0,0:03:00.73,0:03:03.24,Default,,0000,0000,0000,,let me lower the slope.
Dialogue: 0,0:03:03.24,0:03:05.76,Default,,0000,0000,0000,,So if I lower the slope, let's\Nsee, if I lower the y-intercept
Dialogue: 0,0:03:05.76,0:03:09.83,Default,,0000,0000,0000,,a little bit more,\Nis that getting me?
Dialogue: 0,0:03:09.83,0:03:10.65,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:03:10.65,0:03:11.79,Default,,0000,0000,0000,,It got me to those points.
Dialogue: 0,0:03:11.79,0:03:13.96,Default,,0000,0000,0000,,So the equation of the line\Nthat passes through both
Dialogue: 0,0:03:13.96,0:03:17.97,Default,,0000,0000,0000,,of those things is\Nminus 6x minus 22.
Dialogue: 0,0:03:17.97,0:03:20.43,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:03:20.43,0:03:23.74,Default,,0000,0000,0000,,So, once again, it resets it,\Nso I just say the equation 1x
Dialogue: 0,0:03:23.74,0:03:26.54,Default,,0000,0000,0000,,plus 1, but it gives me these\Ntwo new points that I have
Dialogue: 0,0:03:26.54,0:03:28.06,Default,,0000,0000,0000,,to make it go through.
Dialogue: 0,0:03:28.06,0:03:31.48,Default,,0000,0000,0000,,And once again this is going to\Nbe a negative slope, because
Dialogue: 0,0:03:31.48,0:03:34.37,Default,,0000,0000,0000,,for every x that I move\Nforward positive, my y
Dialogue: 0,0:03:34.37,0:03:36.14,Default,,0000,0000,0000,,is actually going down.
Dialogue: 0,0:03:36.14,0:03:38.03,Default,,0000,0000,0000,,So I'm going to have a negative\Nslope here, so let me lower
Dialogue: 0,0:03:38.03,0:03:39.89,Default,,0000,0000,0000,,the slope a little bit.
Dialogue: 0,0:03:39.89,0:03:42.53,Default,,0000,0000,0000,,
Dialogue: 0,0:03:42.53,0:03:44.92,Default,,0000,0000,0000,,It's actually doing fractions,\Nso this thing jumps
Dialogue: 0,0:03:44.92,0:03:45.60,Default,,0000,0000,0000,,around a little bit.
Dialogue: 0,0:03:45.60,0:03:47.51,Default,,0000,0000,0000,,I should probably change\Nthat a little bit.
Dialogue: 0,0:03:47.51,0:03:50.21,Default,,0000,0000,0000,,That looks about right, so let\Nme shift the graph down a
Dialogue: 0,0:03:50.21,0:03:54.17,Default,,0000,0000,0000,,little bit by lowering\Nits y-intercept.
Dialogue: 0,0:03:54.17,0:04:00.42,Default,,0000,0000,0000,,By lowering its y-intercept,\Ncan I hit those two points?
Dialogue: 0,0:04:00.42,0:04:01.41,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:04:01.41,0:04:03.89,Default,,0000,0000,0000,,This is the equation of that\Nline that goes to the points
Dialogue: 0,0:04:03.89,0:04:08.67,Default,,0000,0000,0000,,minus 5,1 and the\Npoints 9,minus 9.
Dialogue: 0,0:04:08.67,0:04:11.34,Default,,0000,0000,0000,,You have a slope of minus 5/7.
Dialogue: 0,0:04:11.34,0:04:15.14,Default,,0000,0000,0000,,For every 7 you go to the\Nright, you go down 5.
Dialogue: 0,0:04:15.14,0:04:18.98,Default,,0000,0000,0000,,If you go 1, 2, 3, 4, 5,\N6, 7, you're going to
Dialogue: 0,0:04:18.98,0:04:22.84,Default,,0000,0000,0000,,go down 1, 2, 3, 4, 5.
Dialogue: 0,0:04:22.84,0:04:25.04,Default,,0000,0000,0000,,And that, we definitely\Nsee that on that line.
Dialogue: 0,0:04:25.04,0:04:27.98,Default,,0000,0000,0000,,And then the y-intercept is\Nminus 18 over 7, which is a
Dialogue: 0,0:04:27.98,0:04:30.27,Default,,0000,0000,0000,,little over 2, it's about a\Nlittle over-- it's what,
Dialogue: 0,0:04:30.27,0:04:32.01,Default,,0000,0000,0000,,a little over 2 and 1/2.
Dialogue: 0,0:04:32.01,0:04:34.05,Default,,0000,0000,0000,,And we see right there\Nthat the y-intercept is
Dialogue: 0,0:04:34.05,0:04:35.42,Default,,0000,0000,0000,,a little over 2 and 1/2.
Dialogue: 0,0:04:35.42,0:04:37.34,Default,,0000,0000,0000,,That's the equation\Nfor our line.
Dialogue: 0,0:04:37.34,0:04:38.86,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:04:38.86,0:04:41.17,Default,,0000,0000,0000,,This is a fun module, because\Nthere are no wrong answers.
Dialogue: 0,0:04:41.17,0:04:43.58,Default,,0000,0000,0000,,You can just keep messing with\Nit until you eventually get
Dialogue: 0,0:04:43.58,0:04:46.57,Default,,0000,0000,0000,,that line to go through both of\Nthose points, but the idea is
Dialogue: 0,0:04:46.57,0:04:49.67,Default,,0000,0000,0000,,really give you that intuition\Nthat the slope is just what the
Dialogue: 0,0:04:49.67,0:04:53.56,Default,,0000,0000,0000,,inclination of the line is, and\Nthen the y-intercept is how far
Dialogue: 0,0:04:53.56,0:04:54.90,Default,,0000,0000,0000,,up and down it gets shifted.
Dialogue: 0,0:04:54.90,0:04:57.11,Default,,0000,0000,0000,,So this is going to be\Na positive slope, but
Dialogue: 0,0:04:57.11,0:04:58.49,Default,,0000,0000,0000,,not as high as 1.
Dialogue: 0,0:04:58.49,0:05:06.51,Default,,0000,0000,0000,,It looks like, for every 1, 2,\N3, 4, 5, 6, 7, 8, 9, 10, 11,
Dialogue: 0,0:05:06.51,0:05:08.44,Default,,0000,0000,0000,,12, for every 12 we go to the\Nright, we're going
Dialogue: 0,0:05:08.44,0:05:11.81,Default,,0000,0000,0000,,to go 1, 2, 3 up.
Dialogue: 0,0:05:11.81,0:05:15.26,Default,,0000,0000,0000,,So our slope is going to be 3\Nover 12, which is also 1 over
Dialogue: 0,0:05:15.26,0:05:17.07,Default,,0000,0000,0000,,4, and we can just look\Nat that visually.
Dialogue: 0,0:05:17.07,0:05:18.68,Default,,0000,0000,0000,,Let's lower our slope.
Dialogue: 0,0:05:18.68,0:05:20.75,Default,,0000,0000,0000,,That's 3/4, not low enough.
Dialogue: 0,0:05:20.75,0:05:22.58,Default,,0000,0000,0000,,1/2, not low enough.
Dialogue: 0,0:05:22.58,0:05:26.06,Default,,0000,0000,0000,,1/4, which I just figured out\Nit is, that looks right, and
Dialogue: 0,0:05:26.06,0:05:29.02,Default,,0000,0000,0000,,then we have to lower\Nthe y-intercept.
Dialogue: 0,0:05:29.02,0:05:32.47,Default,,0000,0000,0000,,We're shifting it down,\Nand there we go.
Dialogue: 0,0:05:32.47,0:05:36.84,Default,,0000,0000,0000,,So the equation of this line,\Nits slope is 1/4, so the
Dialogue: 0,0:05:36.84,0:05:40.15,Default,,0000,0000,0000,,equation of the line\Nis 1/4x plus 1/4.
Dialogue: 0,0:05:40.15,0:05:43.22,Default,,0000,0000,0000,,So hopefully, for those of you\Ntrying to do this module, that,
Dialogue: 0,0:05:43.22,0:05:46.06,Default,,0000,0000,0000,,1, explained how to do it, and\Nfor those of you who don't even
Dialogue: 0,0:05:46.06,0:05:47.98,Default,,0000,0000,0000,,know what this module is, it\Nhopefully gives you a little
Dialogue: 0,0:05:47.98,0:05:52.07,Default,,0000,0000,0000,,intuition about what the slope\Nand the y-intercept do
Dialogue: 0,0:05:52.07,0:05:54.04,Default,,0000,0000,0000,,to an actual line.