[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.98,Default,,0000,0000,0000,,- [Instructor] We are asked,
Dialogue: 0,0:00:00.98,0:00:05.07,Default,,0000,0000,0000,,what is the slope of the line\Nthat contains these points?
Dialogue: 0,0:00:05.07,0:00:07.44,Default,,0000,0000,0000,,So pause this video and see\Nif you can work through this
Dialogue: 0,0:00:07.44,0:00:10.06,Default,,0000,0000,0000,,on your own before we do it together.
Dialogue: 0,0:00:10.06,0:00:11.76,Default,,0000,0000,0000,,Alright, now let's do it together,
Dialogue: 0,0:00:11.76,0:00:14.27,Default,,0000,0000,0000,,and let's just remind\Nourselves what slope is.
Dialogue: 0,0:00:14.27,0:00:19.06,Default,,0000,0000,0000,,Slope is equal to change in y,
Dialogue: 0,0:00:19.06,0:00:21.09,Default,,0000,0000,0000,,this is the Greek letter delta,
Dialogue: 0,0:00:21.09,0:00:21.98,Default,,0000,0000,0000,,look likes a triangle,
Dialogue: 0,0:00:21.98,0:00:24.41,Default,,0000,0000,0000,,but it's shorthand for change in y
Dialogue: 0,0:00:24.41,0:00:27.37,Default,,0000,0000,0000,,over change in x.
Dialogue: 0,0:00:27.37,0:00:31.52,Default,,0000,0000,0000,,Sometimes you would see\Nit written as y2 minus y1
Dialogue: 0,0:00:31.52,0:00:34.81,Default,,0000,0000,0000,,over x2 minus x1
Dialogue: 0,0:00:34.81,0:00:37.61,Default,,0000,0000,0000,,where you could kind of view\Nx1 y1 as the starting point
Dialogue: 0,0:00:37.61,0:00:40.86,Default,,0000,0000,0000,,and x2 y2 as the ending point.
Dialogue: 0,0:00:40.86,0:00:44.79,Default,,0000,0000,0000,,So let's just pick two xy pairs here,
Dialogue: 0,0:00:44.79,0:00:46.14,Default,,0000,0000,0000,,and we can actually pick any two
Dialogue: 0,0:00:46.14,0:00:49.12,Default,,0000,0000,0000,,if we can assume that this is\Nactually describing a line.
Dialogue: 0,0:00:49.12,0:00:51.10,Default,,0000,0000,0000,,So we might as well\Njust pick the first two.
Dialogue: 0,0:00:51.10,0:00:52.89,Default,,0000,0000,0000,,So let's say that's our starting point
Dialogue: 0,0:00:52.89,0:00:54.33,Default,,0000,0000,0000,,and that's our finishing point.
Dialogue: 0,0:00:54.33,0:00:56.69,Default,,0000,0000,0000,,So what is our change in x here?
Dialogue: 0,0:00:56.69,0:00:59.22,Default,,0000,0000,0000,,So we're going from two to three,
Dialogue: 0,0:00:59.22,0:01:03.09,Default,,0000,0000,0000,,so our change in x is\Nequal to three minus two
Dialogue: 0,0:01:03.09,0:01:03.95,Default,,0000,0000,0000,,which is equal to one,
Dialogue: 0,0:01:03.95,0:01:05.55,Default,,0000,0000,0000,,and you can see that\Nto go from two to three
Dialogue: 0,0:01:05.55,0:01:06.74,Default,,0000,0000,0000,,you're just adding one.
Dialogue: 0,0:01:06.74,0:01:08.18,Default,,0000,0000,0000,,And what's our change in y?
Dialogue: 0,0:01:08.18,0:01:10.91,Default,,0000,0000,0000,,Our change in y is our finishing y one
Dialogue: 0,0:01:10.91,0:01:15.00,Default,,0000,0000,0000,,minus our starting y four, which\Nis equal to negative three.
Dialogue: 0,0:01:15.00,0:01:16.97,Default,,0000,0000,0000,,And you could of, you didn't\Neven have to do this math,
Dialogue: 0,0:01:16.97,0:01:17.80,Default,,0000,0000,0000,,you would have been able to see
Dialogue: 0,0:01:17.80,0:01:19.61,Default,,0000,0000,0000,,to go from two to three you added one,
Dialogue: 0,0:01:19.61,0:01:22.60,Default,,0000,0000,0000,,and to go from four to one,\Nyou have to subtract three.
Dialogue: 0,0:01:22.60,0:01:25.05,Default,,0000,0000,0000,,For there we have all\Nthe information we need.
Dialogue: 0,0:01:25.05,0:01:27.80,Default,,0000,0000,0000,,What is change in y over change in x?
Dialogue: 0,0:01:27.80,0:01:29.40,Default,,0000,0000,0000,,Well, it's going to be,
Dialogue: 0,0:01:29.40,0:01:31.56,Default,,0000,0000,0000,,our change in y is negative three
Dialogue: 0,0:01:31.56,0:01:33.08,Default,,0000,0000,0000,,and our change in x is one.
Dialogue: 0,0:01:33.08,0:01:34.100,Default,,0000,0000,0000,,So our slope is negative\Nthree divided by one
Dialogue: 0,0:01:34.100,0:01:37.01,Default,,0000,0000,0000,,is negative three.
Dialogue: 0,0:01:37.01,0:01:38.66,Default,,0000,0000,0000,,Let's do another example.
Dialogue: 0,0:01:39.93,0:01:42.74,Default,,0000,0000,0000,,Here we are asked, what is the slope
Dialogue: 0,0:01:42.74,0:01:45.32,Default,,0000,0000,0000,,of the line that contains these points?
Dialogue: 0,0:01:45.32,0:01:47.41,Default,,0000,0000,0000,,So pause this video and see\Nif you can figure it out
Dialogue: 0,0:01:47.41,0:01:50.72,Default,,0000,0000,0000,,or pause the video again and\Nsee if you can figure it out.
Dialogue: 0,0:01:50.72,0:01:55.72,Default,,0000,0000,0000,,Alright, so remember, slope\Nis equal to change in y
Dialogue: 0,0:01:55.88,0:01:57.61,Default,,0000,0000,0000,,over change in x.
Dialogue: 0,0:01:57.61,0:02:00.23,Default,,0000,0000,0000,,And we should be able to\Npick any two of these pairs
Dialogue: 0,0:02:00.23,0:02:01.99,Default,,0000,0000,0000,,in order to figure that out if we assume
Dialogue: 0,0:02:01.99,0:02:03.51,Default,,0000,0000,0000,,that this is indeed a line.
Dialogue: 0,0:02:03.51,0:02:07.71,Default,,0000,0000,0000,,Well, just for variety, let's\Npick these middle two pairs.
Dialogue: 0,0:02:07.71,0:02:09.73,Default,,0000,0000,0000,,So what's our change in x?
Dialogue: 0,0:02:09.73,0:02:12.26,Default,,0000,0000,0000,,To go from one to five, we added four.
Dialogue: 0,0:02:12.26,0:02:13.73,Default,,0000,0000,0000,,And what's our change in y?
Dialogue: 0,0:02:13.73,0:02:16.92,Default,,0000,0000,0000,,To go from seven to 13, we added six.
Dialogue: 0,0:02:16.92,0:02:21.92,Default,,0000,0000,0000,,So our change in y is six\Nwhen our change in x is four.
Dialogue: 0,0:02:22.77,0:02:25.97,Default,,0000,0000,0000,,And I got the signs right,\Nin both case it's a positive.
Dialogue: 0,0:02:25.97,0:02:28.29,Default,,0000,0000,0000,,When x increases, y increased as well.
Dialogue: 0,0:02:28.29,0:02:29.56,Default,,0000,0000,0000,,So our slope is six fourths,
Dialogue: 0,0:02:29.56,0:02:31.25,Default,,0000,0000,0000,,and we could rewrite that if we like.
Dialogue: 0,0:02:31.25,0:02:33.04,Default,,0000,0000,0000,,Both six and four are divisible by two,
Dialogue: 0,0:02:33.04,0:02:35.28,Default,,0000,0000,0000,,so let be divide both the\Nnumerator and the denominator
Dialogue: 0,0:02:35.28,0:02:38.14,Default,,0000,0000,0000,,by two and we get three\Nhalves, and we're done.