[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.45,0:00:03.57,Default,,0000,0000,0000,,In this video I'm going to do a\Nbunch of examples of finding
Dialogue: 0,0:00:03.57,0:00:07.17,Default,,0000,0000,0000,,the equations of lines in\Nslope-intercept form.
Dialogue: 0,0:00:07.17,0:00:09.61,Default,,0000,0000,0000,,Just as a bit of a review, that\Nmeans equations of lines
Dialogue: 0,0:00:09.61,0:00:17.05,Default,,0000,0000,0000,,in the form of y is equal to mx\Nplus b where m is the slope
Dialogue: 0,0:00:17.05,0:00:21.20,Default,,0000,0000,0000,,and b is the y-intercept.
Dialogue: 0,0:00:21.20,0:00:24.87,Default,,0000,0000,0000,,So let's just do a bunch of\Nthese problems. So here they
Dialogue: 0,0:00:24.87,0:00:28.90,Default,,0000,0000,0000,,tell us that a line has a slope\Nof negative 5, so m is
Dialogue: 0,0:00:28.90,0:00:30.74,Default,,0000,0000,0000,,equal to negative 5.
Dialogue: 0,0:00:30.74,0:00:34.29,Default,,0000,0000,0000,,And it has a y-intercept of 6.
Dialogue: 0,0:00:34.29,0:00:36.30,Default,,0000,0000,0000,,So b is equal to 6.
Dialogue: 0,0:00:36.30,0:00:37.98,Default,,0000,0000,0000,,So this is pretty\Nstraightforward.
Dialogue: 0,0:00:37.98,0:00:41.53,Default,,0000,0000,0000,,The equation of this line\Nis y is equal to
Dialogue: 0,0:00:41.53,0:00:47.55,Default,,0000,0000,0000,,negative 5x plus 6.
Dialogue: 0,0:00:47.55,0:00:49.57,Default,,0000,0000,0000,,That wasn't too bad.
Dialogue: 0,0:00:49.57,0:00:51.57,Default,,0000,0000,0000,,Let's do this next\None over here.
Dialogue: 0,0:00:51.57,0:00:54.30,Default,,0000,0000,0000,,The line has a slope of negative\N1 and contains the
Dialogue: 0,0:00:54.30,0:00:57.32,Default,,0000,0000,0000,,point 4/5 comma 0.
Dialogue: 0,0:00:57.32,0:01:00.60,Default,,0000,0000,0000,,So they're telling us the slope,\Nslope of negative 1.
Dialogue: 0,0:01:00.60,0:01:05.23,Default,,0000,0000,0000,,So we know that m is equal to\Nnegative 1, but we're not 100%
Dialogue: 0,0:01:05.23,0:01:09.19,Default,,0000,0000,0000,,sure about where the y-intercept\Nis just yet.
Dialogue: 0,0:01:09.19,0:01:12.51,Default,,0000,0000,0000,,So we know that this equation\Nis going to be of the form y
Dialogue: 0,0:01:12.51,0:01:19.30,Default,,0000,0000,0000,,is equal to the slope negative\N1x plus b, where b is the
Dialogue: 0,0:01:19.30,0:01:20.46,Default,,0000,0000,0000,,y-intercept.
Dialogue: 0,0:01:20.46,0:01:23.65,Default,,0000,0000,0000,,Now, we can use this coordinate\Ninformation, the
Dialogue: 0,0:01:23.65,0:01:25.87,Default,,0000,0000,0000,,fact that it contains this\Npoint, we can use that
Dialogue: 0,0:01:25.87,0:01:28.59,Default,,0000,0000,0000,,information to solve for b.
Dialogue: 0,0:01:28.59,0:01:31.53,Default,,0000,0000,0000,,The fact that the line contains\Nthis point means that
Dialogue: 0,0:01:31.53,0:01:37.69,Default,,0000,0000,0000,,the value x is equal to 4/5, y\Nis equal to 0 must satisfy
Dialogue: 0,0:01:37.69,0:01:38.26,Default,,0000,0000,0000,,this equation.
Dialogue: 0,0:01:38.26,0:01:43.12,Default,,0000,0000,0000,,So let's substitute those in.\Ny is equal to 0 when x is
Dialogue: 0,0:01:43.12,0:01:44.09,Default,,0000,0000,0000,,equal to 4/5.
Dialogue: 0,0:01:44.09,0:01:50.17,Default,,0000,0000,0000,,So 0 is equal to negative\N1 times 4/5 plus b.
Dialogue: 0,0:01:50.17,0:01:52.81,Default,,0000,0000,0000,,I'll scroll down a little bit.
Dialogue: 0,0:01:52.81,0:01:58.11,Default,,0000,0000,0000,,So let's see, we get a 0 is\Nequal to negative 4/5 plus b.
Dialogue: 0,0:01:58.11,0:02:02.04,Default,,0000,0000,0000,,We can add 4/5 to both sides\Nof this equation.
Dialogue: 0,0:02:02.04,0:02:04.25,Default,,0000,0000,0000,,So we get add a 4/5 there.
Dialogue: 0,0:02:04.25,0:02:07.32,Default,,0000,0000,0000,,We could add a 4/5 to\Nthat side as well.
Dialogue: 0,0:02:07.32,0:02:10.10,Default,,0000,0000,0000,,The whole reason I did that is\Nso that cancels out with that.
Dialogue: 0,0:02:10.10,0:02:12.13,Default,,0000,0000,0000,,You get b is equal to 4/5.
Dialogue: 0,0:02:16.25,0:02:19.18,Default,,0000,0000,0000,,So we now have the equation\Nof the line.
Dialogue: 0,0:02:19.18,0:02:23.04,Default,,0000,0000,0000,,y is equal to negative 1 times\Nx, which we write as negative
Dialogue: 0,0:02:23.04,0:02:32.50,Default,,0000,0000,0000,,x, plus b, which is 4/5,\Njust like that.
Dialogue: 0,0:02:32.50,0:02:34.48,Default,,0000,0000,0000,,Now we have this one.
Dialogue: 0,0:02:34.48,0:02:39.58,Default,,0000,0000,0000,,The line contains the point\N2 comma 6 and 5 comma 0.
Dialogue: 0,0:02:39.58,0:02:42.54,Default,,0000,0000,0000,,So they haven't given us the\Nslope or the y-intercept
Dialogue: 0,0:02:42.54,0:02:43.03,Default,,0000,0000,0000,,explicitly.
Dialogue: 0,0:02:43.03,0:02:45.35,Default,,0000,0000,0000,,But we could figure out both\Nof them from these
Dialogue: 0,0:02:45.35,0:02:45.65,Default,,0000,0000,0000,,coordinates.
Dialogue: 0,0:02:45.65,0:02:48.27,Default,,0000,0000,0000,,So the first thing we can do\Nis figure out the slope.
Dialogue: 0,0:02:48.27,0:02:53.75,Default,,0000,0000,0000,,So we know that the slope m is\Nequal to change in y over
Dialogue: 0,0:02:53.75,0:02:58.10,Default,,0000,0000,0000,,change in x, which is equal to--\NWhat is the change in y?
Dialogue: 0,0:02:58.10,0:02:59.49,Default,,0000,0000,0000,,Let's start with this\None right here.
Dialogue: 0,0:02:59.49,0:03:00.98,Default,,0000,0000,0000,,So we do 6 minus 0.
Dialogue: 0,0:03:04.21,0:03:05.07,Default,,0000,0000,0000,,Let me do it this way.
Dialogue: 0,0:03:05.07,0:03:10.41,Default,,0000,0000,0000,,So that's a 6-- I want to make\Nit color-coded-- minus 0.
Dialogue: 0,0:03:10.41,0:03:14.34,Default,,0000,0000,0000,,So 6 minus 0, that's\Nour change in y.
Dialogue: 0,0:03:14.34,0:03:24.19,Default,,0000,0000,0000,,Our change in x is 2\Nminus 2 minus 5.
Dialogue: 0,0:03:24.19,0:03:26.32,Default,,0000,0000,0000,,The reason why I color-coded\Nit is I wanted to show you
Dialogue: 0,0:03:26.32,0:03:30.89,Default,,0000,0000,0000,,when I used this y term first,\NI used the 6 up here, that I
Dialogue: 0,0:03:30.89,0:03:33.38,Default,,0000,0000,0000,,have to use this x term\Nfirst as well.
Dialogue: 0,0:03:33.38,0:03:36.73,Default,,0000,0000,0000,,So I wanted to show you, this\Nis the coordinate 2 comma 6.
Dialogue: 0,0:03:36.73,0:03:38.59,Default,,0000,0000,0000,,This is the coordinate\N5 comma 0.
Dialogue: 0,0:03:38.59,0:03:41.65,Default,,0000,0000,0000,,I couldn't have swapped\Nthe 2 and the 5 then.
Dialogue: 0,0:03:41.65,0:03:45.03,Default,,0000,0000,0000,,Then I would have gotten the\Nnegative of the answer.
Dialogue: 0,0:03:45.03,0:03:46.08,Default,,0000,0000,0000,,But what do we get here?
Dialogue: 0,0:03:46.08,0:03:51.21,Default,,0000,0000,0000,,This is equal to\N6 minus 0 is 6.
Dialogue: 0,0:03:51.21,0:03:54.77,Default,,0000,0000,0000,,2 minus 5 is negative 3.
Dialogue: 0,0:03:54.77,0:03:58.91,Default,,0000,0000,0000,,So this becomes negative 6\Nover 3, which is the same
Dialogue: 0,0:03:58.91,0:04:01.31,Default,,0000,0000,0000,,thing as negative 2.
Dialogue: 0,0:04:01.31,0:04:02.25,Default,,0000,0000,0000,,So that's our slope.
Dialogue: 0,0:04:02.25,0:04:06.92,Default,,0000,0000,0000,,So, so far we know that the line\Nmust be, y is equal to
Dialogue: 0,0:04:06.92,0:04:12.58,Default,,0000,0000,0000,,the slope-- I'll do that in\Norange-- negative 2 times x
Dialogue: 0,0:04:12.58,0:04:15.16,Default,,0000,0000,0000,,plus our y-intercept.
Dialogue: 0,0:04:15.16,0:04:17.78,Default,,0000,0000,0000,,Now we can do exactly what we\Ndid in the last problem.
Dialogue: 0,0:04:17.78,0:04:20.58,Default,,0000,0000,0000,,We can use one of these\Npoints to solve for b.
Dialogue: 0,0:04:20.58,0:04:22.03,Default,,0000,0000,0000,,We can use either one.
Dialogue: 0,0:04:22.03,0:04:25.92,Default,,0000,0000,0000,,Both of these are on the line,\Nso both of these must satisfy
Dialogue: 0,0:04:25.92,0:04:26.90,Default,,0000,0000,0000,,this equation.
Dialogue: 0,0:04:26.90,0:04:29.80,Default,,0000,0000,0000,,I'll use the 5 comma 0 because\Nit's always nice when
Dialogue: 0,0:04:29.80,0:04:31.02,Default,,0000,0000,0000,,you have a 0 there.
Dialogue: 0,0:04:31.02,0:04:32.82,Default,,0000,0000,0000,,The math is a little\Nbit easier.
Dialogue: 0,0:04:32.82,0:04:34.51,Default,,0000,0000,0000,,So let's put the 5\Ncomma 0 there.
Dialogue: 0,0:04:34.51,0:04:38.90,Default,,0000,0000,0000,,So y is equal to 0 when\Nx is equal to 5.
Dialogue: 0,0:04:38.90,0:04:43.82,Default,,0000,0000,0000,,So y is equal to 0 when you have\Nnegative 2 times 5, when
Dialogue: 0,0:04:43.82,0:04:47.70,Default,,0000,0000,0000,,x is equal to 5 plus b.
Dialogue: 0,0:04:47.70,0:04:52.65,Default,,0000,0000,0000,,So you get 0 is equal\Nto -10 plus b.
Dialogue: 0,0:04:52.65,0:04:57.82,Default,,0000,0000,0000,,If you add 10 to both sides of\Nthis equation, let's add 10 to
Dialogue: 0,0:04:57.82,0:05:00.68,Default,,0000,0000,0000,,both sides, these\Ntwo cancel out.
Dialogue: 0,0:05:00.68,0:05:03.97,Default,,0000,0000,0000,,You get b is equal to\N10 plus 0 or 10.
Dialogue: 0,0:05:03.97,0:05:06.42,Default,,0000,0000,0000,,So you get b is equal to 10.
Dialogue: 0,0:05:06.42,0:05:07.94,Default,,0000,0000,0000,,Now we know the equation\Nfor the line.
Dialogue: 0,0:05:07.94,0:05:14.11,Default,,0000,0000,0000,,The equation is y-- let me do it\Nin a new color-- y is equal
Dialogue: 0,0:05:14.11,0:05:22.28,Default,,0000,0000,0000,,to negative 2x plus b plus 10.
Dialogue: 0,0:05:22.28,0:05:23.47,Default,,0000,0000,0000,,We are done.
Dialogue: 0,0:05:23.47,0:05:24.72,Default,,0000,0000,0000,,Let's do another one of these.
Dialogue: 0,0:05:28.18,0:05:31.27,Default,,0000,0000,0000,,All right, the line contains\Nthe points 3 comma 5 and
Dialogue: 0,0:05:31.27,0:05:32.89,Default,,0000,0000,0000,,negative 3 comma 0.
Dialogue: 0,0:05:32.89,0:05:36.38,Default,,0000,0000,0000,,Just like the last problem, we\Nstart by figuring out the
Dialogue: 0,0:05:36.38,0:05:40.38,Default,,0000,0000,0000,,slope, which we will call m.
Dialogue: 0,0:05:40.38,0:05:44.83,Default,,0000,0000,0000,,It's the same thing as the rise\Nover the run, which is
Dialogue: 0,0:05:44.83,0:05:48.19,Default,,0000,0000,0000,,the same thing as the change\Nin y over the change in x.
Dialogue: 0,0:05:48.19,0:05:50.07,Default,,0000,0000,0000,,If you were doing this for your\Nhomework, you wouldn't
Dialogue: 0,0:05:50.07,0:05:50.87,Default,,0000,0000,0000,,have to write all this.
Dialogue: 0,0:05:50.87,0:05:52.92,Default,,0000,0000,0000,,I just want to make sure that\Nyou understand that these are
Dialogue: 0,0:05:52.92,0:05:55.15,Default,,0000,0000,0000,,all the same things.
Dialogue: 0,0:05:55.15,0:05:58.52,Default,,0000,0000,0000,,Then what is our change in\Ny over our change in x?
Dialogue: 0,0:05:58.52,0:06:02.28,Default,,0000,0000,0000,,This is equal to, let's start\Nwith the side first. It's just
Dialogue: 0,0:06:02.28,0:06:03.98,Default,,0000,0000,0000,,to show you I could pick\Neither of these points.
Dialogue: 0,0:06:03.98,0:06:14.05,Default,,0000,0000,0000,,So let's say it's 0 minus\N5 just like that.
Dialogue: 0,0:06:14.05,0:06:17.00,Default,,0000,0000,0000,,So I'm using this coordinate\Nfirst. I'm kind of viewing it
Dialogue: 0,0:06:17.00,0:06:19.77,Default,,0000,0000,0000,,as the endpoint.
Dialogue: 0,0:06:19.77,0:06:22.42,Default,,0000,0000,0000,,Remember when I first learned\Nthis, I would always be
Dialogue: 0,0:06:22.42,0:06:24.16,Default,,0000,0000,0000,,tempted to do the x\Nin the numerator.
Dialogue: 0,0:06:24.16,0:06:25.99,Default,,0000,0000,0000,,No, you use the y's\Nin the numerator.
Dialogue: 0,0:06:25.99,0:06:28.47,Default,,0000,0000,0000,,So that's the second\Nof the coordinates.
Dialogue: 0,0:06:28.47,0:06:38.44,Default,,0000,0000,0000,,That is going to be over\Nnegative 3 minus 3.
Dialogue: 0,0:06:41.25,0:06:44.37,Default,,0000,0000,0000,,This is the coordinate\Nnegative 3, 0.
Dialogue: 0,0:06:44.37,0:06:46.42,Default,,0000,0000,0000,,This is the coordinate 3, 5.
Dialogue: 0,0:06:46.42,0:06:47.98,Default,,0000,0000,0000,,We're subtracting that.
Dialogue: 0,0:06:47.98,0:06:49.31,Default,,0000,0000,0000,,So what are we going to get?
Dialogue: 0,0:06:49.31,0:06:52.57,Default,,0000,0000,0000,,This is going to be equal to--\NI'll do it in a neutral
Dialogue: 0,0:06:52.57,0:06:56.21,Default,,0000,0000,0000,,color-- this is going to be\Nequal to the numerator is
Dialogue: 0,0:06:56.21,0:07:02.01,Default,,0000,0000,0000,,negative 5 over negative 3\Nminus 3 is negative 6.
Dialogue: 0,0:07:02.01,0:07:03.65,Default,,0000,0000,0000,,So the negatives cancel out.
Dialogue: 0,0:07:03.65,0:07:05.93,Default,,0000,0000,0000,,You get 5/6.
Dialogue: 0,0:07:05.93,0:07:08.70,Default,,0000,0000,0000,,So we know that the equation is\Ngoing to be of the form y
Dialogue: 0,0:07:08.70,0:07:15.56,Default,,0000,0000,0000,,is equal to 5/6 x plus b.
Dialogue: 0,0:07:15.56,0:07:18.60,Default,,0000,0000,0000,,Now we can substitute one of\Nthese coordinates in for b.
Dialogue: 0,0:07:18.60,0:07:19.44,Default,,0000,0000,0000,,So let's do.
Dialogue: 0,0:07:19.44,0:07:21.31,Default,,0000,0000,0000,,I always like to use the one\Nthat has the 0 in it.
Dialogue: 0,0:07:21.31,0:07:33.27,Default,,0000,0000,0000,,So y is a zero when x is\Nnegative 3 plus b.
Dialogue: 0,0:07:33.27,0:07:37.81,Default,,0000,0000,0000,,So all I did is I substituted\Nnegative 3 for x, 0 for y.
Dialogue: 0,0:07:37.81,0:07:40.86,Default,,0000,0000,0000,,I know I can do that because\Nthis is on the line.
Dialogue: 0,0:07:40.86,0:07:44.04,Default,,0000,0000,0000,,This must satisfy the equation\Nof the line.
Dialogue: 0,0:07:44.04,0:07:45.60,Default,,0000,0000,0000,,Let's solve for b.
Dialogue: 0,0:07:45.60,0:07:49.99,Default,,0000,0000,0000,,So we get zero is equal to, well\Nif we divide negative 3
Dialogue: 0,0:07:49.99,0:07:51.83,Default,,0000,0000,0000,,by 3, that becomes a 1.
Dialogue: 0,0:07:51.83,0:07:54.89,Default,,0000,0000,0000,,If you divide 6 by 3,\Nthat becomes a 2.
Dialogue: 0,0:07:54.89,0:08:02.38,Default,,0000,0000,0000,,So it becomes negative\N5/2 plus b.
Dialogue: 0,0:08:02.38,0:08:05.28,Default,,0000,0000,0000,,We could add 5/2 to both\Nsides of the equation,
Dialogue: 0,0:08:05.28,0:08:08.63,Default,,0000,0000,0000,,plus 5/2, plus 5/2.
Dialogue: 0,0:08:08.63,0:08:10.85,Default,,0000,0000,0000,,I like to change my notation\Njust so you get
Dialogue: 0,0:08:10.85,0:08:12.52,Default,,0000,0000,0000,,familiar with both.
Dialogue: 0,0:08:12.52,0:08:17.80,Default,,0000,0000,0000,,So the equation becomes 5/2 is\Nequal to-- that's a 0-- is
Dialogue: 0,0:08:17.80,0:08:19.60,Default,,0000,0000,0000,,equal to b.
Dialogue: 0,0:08:19.60,0:08:22.09,Default,,0000,0000,0000,,b is 5/2.
Dialogue: 0,0:08:22.09,0:08:31.94,Default,,0000,0000,0000,,So the equation of our line is\Ny is equal to 5/6 x plus b,
Dialogue: 0,0:08:31.94,0:08:37.82,Default,,0000,0000,0000,,which we just figured out\Nis 5/2, plus 5/2.
Dialogue: 0,0:08:37.82,0:08:38.71,Default,,0000,0000,0000,,We are done.
Dialogue: 0,0:08:38.71,0:08:41.28,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:08:41.28,0:08:43.50,Default,,0000,0000,0000,,We have a graph here.
Dialogue: 0,0:08:43.50,0:08:45.30,Default,,0000,0000,0000,,Let's figure out the equation\Nof this graph.
Dialogue: 0,0:08:45.30,0:08:46.90,Default,,0000,0000,0000,,This is actually, on some level,\Na little bit easier.
Dialogue: 0,0:08:46.90,0:08:47.74,Default,,0000,0000,0000,,What's the slope?
Dialogue: 0,0:08:47.74,0:08:52.25,Default,,0000,0000,0000,,Slope is change in y\Nover change it x.
Dialogue: 0,0:08:52.25,0:08:53.31,Default,,0000,0000,0000,,So let's see what happens.
Dialogue: 0,0:08:53.31,0:08:57.90,Default,,0000,0000,0000,,When we move in x, when our\Nchange in x is 1, so that is
Dialogue: 0,0:08:57.90,0:08:58.94,Default,,0000,0000,0000,,our change in x.
Dialogue: 0,0:08:58.94,0:09:00.85,Default,,0000,0000,0000,,So change in x is 1.
Dialogue: 0,0:09:00.85,0:09:04.13,Default,,0000,0000,0000,,I'm just deciding to change\Nmy x by 1, increment by 1.
Dialogue: 0,0:09:04.13,0:09:05.90,Default,,0000,0000,0000,,What is the change in y?
Dialogue: 0,0:09:05.90,0:09:10.39,Default,,0000,0000,0000,,It looks like y changes\Nexactly by 4.
Dialogue: 0,0:09:10.39,0:09:14.98,Default,,0000,0000,0000,,It looks like my delta y, my\Nchange in y, is equal to 4
Dialogue: 0,0:09:14.98,0:09:20.69,Default,,0000,0000,0000,,when my delta x is equal to 1.
Dialogue: 0,0:09:20.69,0:09:24.34,Default,,0000,0000,0000,,So change in y over change in\Nx, change in y is 4 when
Dialogue: 0,0:09:24.34,0:09:26.22,Default,,0000,0000,0000,,change in x is 1.
Dialogue: 0,0:09:26.22,0:09:30.38,Default,,0000,0000,0000,,So the slope is equal to 4.
Dialogue: 0,0:09:30.38,0:09:32.19,Default,,0000,0000,0000,,Now what's its y-intercept?
Dialogue: 0,0:09:32.19,0:09:33.72,Default,,0000,0000,0000,,Well here we can just\Nlook at the graph.
Dialogue: 0,0:09:33.72,0:09:38.26,Default,,0000,0000,0000,,It looks like it intersects\Ny-axis at y is equal to
Dialogue: 0,0:09:38.26,0:09:41.60,Default,,0000,0000,0000,,negative 6, or at the\Npoint 0, negative 6.
Dialogue: 0,0:09:41.60,0:09:44.18,Default,,0000,0000,0000,,So we know that b is equal\Nto negative 6.
Dialogue: 0,0:09:46.95,0:09:48.88,Default,,0000,0000,0000,,So we know the equation\Nof the line.
Dialogue: 0,0:09:48.88,0:09:56.63,Default,,0000,0000,0000,,The equation of the line is y is\Nequal to the slope times x
Dialogue: 0,0:09:56.63,0:09:59.03,Default,,0000,0000,0000,,plus the y-intercept.
Dialogue: 0,0:09:59.03,0:10:01.85,Default,,0000,0000,0000,,I should write that.
Dialogue: 0,0:10:01.85,0:10:07.84,Default,,0000,0000,0000,,So minus 6, that is plus\Nnegative 6 So that is the
Dialogue: 0,0:10:07.84,0:10:09.80,Default,,0000,0000,0000,,equation of our line.
Dialogue: 0,0:10:09.80,0:10:12.98,Default,,0000,0000,0000,,Let's do one more of these.
Dialogue: 0,0:10:12.98,0:10:17.17,Default,,0000,0000,0000,,So they tell us that f of\N1.5 is negative 3, f of
Dialogue: 0,0:10:17.17,0:10:18.75,Default,,0000,0000,0000,,negative 1 is 2.
Dialogue: 0,0:10:18.75,0:10:19.97,Default,,0000,0000,0000,,What is that?
Dialogue: 0,0:10:19.97,0:10:23.83,Default,,0000,0000,0000,,Well, all this is just a fancy\Nway of telling you that the
Dialogue: 0,0:10:23.83,0:10:30.53,Default,,0000,0000,0000,,point when x is 1.5, when you\Nput 1.5 into the function, the
Dialogue: 0,0:10:30.53,0:10:33.49,Default,,0000,0000,0000,,function evaluates\Nas negative 3.
Dialogue: 0,0:10:33.49,0:10:36.75,Default,,0000,0000,0000,,So this tells us that the\Ncoordinate 1.5, negative 3 is
Dialogue: 0,0:10:36.75,0:10:38.27,Default,,0000,0000,0000,,on the line.
Dialogue: 0,0:10:38.27,0:10:41.96,Default,,0000,0000,0000,,Then this tells us that the\Npoint when x is negative 1, f
Dialogue: 0,0:10:41.96,0:10:44.42,Default,,0000,0000,0000,,of x is equal to 2.
Dialogue: 0,0:10:44.42,0:10:47.54,Default,,0000,0000,0000,,This is just a fancy way of\Nsaying that both of these two
Dialogue: 0,0:10:47.54,0:10:51.40,Default,,0000,0000,0000,,points are on the line,\Nnothing unusual.
Dialogue: 0,0:10:51.40,0:10:54.38,Default,,0000,0000,0000,,I think the point of this\Nproblem is to get you familiar
Dialogue: 0,0:10:54.38,0:10:56.87,Default,,0000,0000,0000,,with function notation, for you\Nto not get intimidated if
Dialogue: 0,0:10:56.87,0:10:57.97,Default,,0000,0000,0000,,you see something like this.
Dialogue: 0,0:10:57.97,0:11:01.54,Default,,0000,0000,0000,,If you evaluate the function\Nat 1.5, you get negative 3.
Dialogue: 0,0:11:01.54,0:11:04.44,Default,,0000,0000,0000,,So that's the coordinate if\Nyou imagine that y is
Dialogue: 0,0:11:04.44,0:11:06.02,Default,,0000,0000,0000,,equal to f of x.
Dialogue: 0,0:11:06.02,0:11:06.95,Default,,0000,0000,0000,,So this would be the\Ny-coordinate.
Dialogue: 0,0:11:06.95,0:11:09.25,Default,,0000,0000,0000,,It would be equal to negative\N3 when x is 1.5.
Dialogue: 0,0:11:09.25,0:11:10.84,Default,,0000,0000,0000,,Anyway, I've said it\Nmultiple times.
Dialogue: 0,0:11:10.84,0:11:13.28,Default,,0000,0000,0000,,Let's figure out the\Nslope of this line.
Dialogue: 0,0:11:13.28,0:11:20.02,Default,,0000,0000,0000,,The slope which is change in y\Nover change in x is equal to,
Dialogue: 0,0:11:20.02,0:11:27.46,Default,,0000,0000,0000,,let's start with 2 minus this\Nguy, negative 3-- these are
Dialogue: 0,0:11:27.46,0:11:32.88,Default,,0000,0000,0000,,the y-values-- over, all\Nof that over, negative
Dialogue: 0,0:11:32.88,0:11:40.14,Default,,0000,0000,0000,,1 minus this guy.
Dialogue: 0,0:11:40.14,0:11:43.33,Default,,0000,0000,0000,,Let me write it this way,\Nnegative 1 minus
Dialogue: 0,0:11:43.33,0:11:48.44,Default,,0000,0000,0000,,that guy, minus 1.5.
Dialogue: 0,0:11:48.44,0:11:50.34,Default,,0000,0000,0000,,I do the colors because I want\Nto show you that the negative
Dialogue: 0,0:11:50.34,0:11:54.06,Default,,0000,0000,0000,,1 and the 2 are both coming from\Nthis, that's why I use
Dialogue: 0,0:11:54.06,0:11:57.50,Default,,0000,0000,0000,,both of them first. If I used\Nthese guys first, I would have
Dialogue: 0,0:11:57.50,0:12:00.50,Default,,0000,0000,0000,,to use both the x and the y\Nfirst. If I use the 2 first, I
Dialogue: 0,0:12:00.50,0:12:02.08,Default,,0000,0000,0000,,have to use the negative\N1 first. That's why I'm
Dialogue: 0,0:12:02.08,0:12:03.39,Default,,0000,0000,0000,,color-coding it.
Dialogue: 0,0:12:03.39,0:12:08.36,Default,,0000,0000,0000,,So this is going to be equal\Nto 2 minus negative 3.
Dialogue: 0,0:12:08.36,0:12:10.37,Default,,0000,0000,0000,,That's the same thing\Nas 2 plus 3.
Dialogue: 0,0:12:10.37,0:12:11.62,Default,,0000,0000,0000,,So that is 5.
Dialogue: 0,0:12:16.48,0:12:20.04,Default,,0000,0000,0000,,Negative 1 minus 1.5\Nis negative 2.5.
Dialogue: 0,0:12:23.83,0:12:27.77,Default,,0000,0000,0000,,5 divided by 2.5\Nis equal to 2.
Dialogue: 0,0:12:27.77,0:12:30.25,Default,,0000,0000,0000,,So the slope of this\Nline is negative 2.
Dialogue: 0,0:12:30.25,0:12:32.13,Default,,0000,0000,0000,,Actually I'll take a little\Naside to show you it doesn't
Dialogue: 0,0:12:32.13,0:12:34.48,Default,,0000,0000,0000,,matter what order\NI do this in.
Dialogue: 0,0:12:34.48,0:12:36.18,Default,,0000,0000,0000,,If I use this coordinate first,\Nthen I have to use that
Dialogue: 0,0:12:36.18,0:12:38.14,Default,,0000,0000,0000,,coordinate first. Let's\Ndo it the other way.
Dialogue: 0,0:12:38.14,0:12:54.18,Default,,0000,0000,0000,,If I did it as negative 3\Nminus 2 over 1.5 minus
Dialogue: 0,0:12:54.18,0:12:59.81,Default,,0000,0000,0000,,negative 1, this should be minus\Nthe 2 over 1.5 minus the
Dialogue: 0,0:12:59.81,0:13:01.06,Default,,0000,0000,0000,,negative 1.
Dialogue: 0,0:13:03.30,0:13:04.78,Default,,0000,0000,0000,,This should give me\Nthe same answer.
Dialogue: 0,0:13:04.78,0:13:06.13,Default,,0000,0000,0000,,This is equal to what?
Dialogue: 0,0:13:06.13,0:13:12.86,Default,,0000,0000,0000,,Negative 3 minus 2 is negative\N5 over 1.5 minus negative 1.
Dialogue: 0,0:13:12.86,0:13:14.52,Default,,0000,0000,0000,,That's 1.5 plus 1.
Dialogue: 0,0:13:14.52,0:13:16.61,Default,,0000,0000,0000,,That's over 2.5.
Dialogue: 0,0:13:16.61,0:13:18.84,Default,,0000,0000,0000,,So once again, this is\Nequal the negative 2.
Dialogue: 0,0:13:18.84,0:13:20.34,Default,,0000,0000,0000,,So I just wanted to show you,\Nit doesn't matter which one
Dialogue: 0,0:13:20.34,0:13:23.09,Default,,0000,0000,0000,,you pick as the starting or\Nthe endpoint, as long as
Dialogue: 0,0:13:23.09,0:13:23.98,Default,,0000,0000,0000,,you're consistent.
Dialogue: 0,0:13:23.98,0:13:26.65,Default,,0000,0000,0000,,If this is the starting y,\Nthis is the starting x.
Dialogue: 0,0:13:26.65,0:13:28.37,Default,,0000,0000,0000,,If this is the finishing\Ny, this has to be
Dialogue: 0,0:13:28.37,0:13:29.50,Default,,0000,0000,0000,,the finishing x.
Dialogue: 0,0:13:29.50,0:13:33.10,Default,,0000,0000,0000,,But anyway, we know that the\Nslope is negative 2.
Dialogue: 0,0:13:33.10,0:13:36.54,Default,,0000,0000,0000,,So we know the equation is y is\Nequal to negative 2x plus
Dialogue: 0,0:13:36.54,0:13:39.17,Default,,0000,0000,0000,,some y-intercept.
Dialogue: 0,0:13:39.17,0:13:40.72,Default,,0000,0000,0000,,Let's use one of these\Ncoordinates.
Dialogue: 0,0:13:40.72,0:13:43.43,Default,,0000,0000,0000,,I'll use this one since it\Ndoesn't have a decimal in it.
Dialogue: 0,0:13:43.43,0:13:47.45,Default,,0000,0000,0000,,So we know that y\Nis equal to 2.
Dialogue: 0,0:13:47.45,0:13:52.63,Default,,0000,0000,0000,,So y is equal to 2 when x\Nis equal to negative 1.
Dialogue: 0,0:13:55.14,0:13:57.29,Default,,0000,0000,0000,,Of course you have\Nyour plus b.
Dialogue: 0,0:13:57.29,0:14:02.71,Default,,0000,0000,0000,,So 2 is equal to negative 2\Ntimes negative 1 is 2 plus b.
Dialogue: 0,0:14:02.71,0:14:06.39,Default,,0000,0000,0000,,If you subtract 2 from both\Nsides of this equation, minus
Dialogue: 0,0:14:06.39,0:14:10.37,Default,,0000,0000,0000,,2, minus 2, you're subtracting\Nit from both sides of this
Dialogue: 0,0:14:10.37,0:14:12.48,Default,,0000,0000,0000,,equation, you're going to get\N0 on the left-hand side is
Dialogue: 0,0:14:12.48,0:14:14.52,Default,,0000,0000,0000,,equal to b.
Dialogue: 0,0:14:14.52,0:14:15.67,Default,,0000,0000,0000,,So b is 0.
Dialogue: 0,0:14:15.67,0:14:18.43,Default,,0000,0000,0000,,So the equation of our\Nline is just y is
Dialogue: 0,0:14:18.43,0:14:19.68,Default,,0000,0000,0000,,equal to negative 2x.
Dialogue: 0,0:14:22.04,0:14:23.87,Default,,0000,0000,0000,,Actually if you wanted to write\Nit in function notation,
Dialogue: 0,0:14:23.87,0:14:28.19,Default,,0000,0000,0000,,it would be that f of x is\Nequal to negative 2x.
Dialogue: 0,0:14:28.19,0:14:30.81,Default,,0000,0000,0000,,I kind of just assumed that\Ny is equal to f of x.
Dialogue: 0,0:14:30.81,0:14:32.42,Default,,0000,0000,0000,,But this is really\Nthe equation.
Dialogue: 0,0:14:32.42,0:14:33.99,Default,,0000,0000,0000,,They never mentioned y's here.
Dialogue: 0,0:14:33.99,0:14:37.89,Default,,0000,0000,0000,,So you could just write f of x\Nis equal to 2x right here.
Dialogue: 0,0:14:37.89,0:14:40.19,Default,,0000,0000,0000,,Each of these coordinates\Nare the coordinates
Dialogue: 0,0:14:40.19,0:14:42.61,Default,,0000,0000,0000,,of x and f of x.
Dialogue: 0,0:14:46.96,0:14:49.96,Default,,0000,0000,0000,,So you could even view the\Ndefinition of slope as change
Dialogue: 0,0:14:49.96,0:14:53.32,Default,,0000,0000,0000,,in f of x over change in x.
Dialogue: 0,0:14:53.32,0:14:57.09,Default,,0000,0000,0000,,These are all equivalent ways\Nof viewing the same thing.