WEBVTT

00:00:00.000 --> 00:00:00.980
- [Instructor] We are asked,

00:00:00.980 --> 00:00:05.070
what is the slope of the line
that contains these points?

00:00:05.070 --> 00:00:07.440
So pause this video and see
if you can work through this

00:00:07.440 --> 00:00:10.060
on your own before we do it together.

00:00:10.060 --> 00:00:11.760
Alright, now let's do it together,

00:00:11.760 --> 00:00:14.270
and let's just remind
ourselves what slope is.

00:00:14.270 --> 00:00:19.060
Slope is equal to change in y,

00:00:19.060 --> 00:00:21.090
this is the Greek letter delta,

00:00:21.090 --> 00:00:21.980
look likes a triangle,

00:00:21.980 --> 00:00:24.410
but it's shorthand for change in y

00:00:24.410 --> 00:00:27.370
over change in x.

00:00:27.370 --> 00:00:31.523
Sometimes you would see
it written as y2 minus y1

00:00:31.523 --> 00:00:34.810
over x2 minus x1

00:00:34.810 --> 00:00:37.610
where you could kind of view
x1 y1 as the starting point

00:00:37.610 --> 00:00:40.862
and x2 y2 as the ending point.

00:00:40.862 --> 00:00:44.790
So let's just pick two xy pairs here,

00:00:44.790 --> 00:00:46.140
and we can actually pick any two

00:00:46.140 --> 00:00:49.120
if we can assume that this is
actually describing a line.

00:00:49.120 --> 00:00:51.100
So we might as well
just pick the first two.

00:00:51.100 --> 00:00:52.890
So let's say that's our starting point

00:00:52.890 --> 00:00:54.332
and that's our finishing point.

00:00:54.332 --> 00:00:56.686
So what is our change in x here?

00:00:56.686 --> 00:00:59.220
So we're going from two to three,

00:00:59.220 --> 00:01:03.090
so our change in x is
equal to three minus two

00:01:03.090 --> 00:01:03.950
which is equal to one,

00:01:03.950 --> 00:01:05.550
and you can see that
to go from two to three

00:01:05.550 --> 00:01:06.740
you're just adding one.

00:01:06.740 --> 00:01:08.182
And what's our change in y?

00:01:08.182 --> 00:01:10.911
Our change in y is our finishing y one

00:01:10.911 --> 00:01:15.000
minus our starting y four, which
is equal to negative three.

00:01:15.000 --> 00:01:16.970
And you could of, you didn't
even have to do this math,

00:01:16.970 --> 00:01:17.803
you would have been able to see

00:01:17.803 --> 00:01:19.610
to go from two to three you added one,

00:01:19.610 --> 00:01:22.602
and to go from four to one,
you have to subtract three.

00:01:22.602 --> 00:01:25.050
For there we have all
the information we need.

00:01:25.050 --> 00:01:27.802
What is change in y over change in x?

00:01:27.802 --> 00:01:29.405
Well, it's going to be,

00:01:29.405 --> 00:01:31.560
our change in y is negative three

00:01:31.560 --> 00:01:33.080
and our change in x is one.

00:01:33.080 --> 00:01:34.999
So our slope is negative
three divided by one

00:01:34.999 --> 00:01:37.007
is negative three.

00:01:37.007 --> 00:01:38.663
Let's do another example.

00:01:39.930 --> 00:01:42.743
Here we are asked, what is the slope

00:01:42.743 --> 00:01:45.320
of the line that contains these points?

00:01:45.320 --> 00:01:47.410
So pause this video and see
if you can figure it out

00:01:47.410 --> 00:01:50.720
or pause the video again and
see if you can figure it out.

00:01:50.720 --> 00:01:55.720
Alright, so remember, slope
is equal to change in y

00:01:55.876 --> 00:01:57.610
over change in x.

00:01:57.610 --> 00:02:00.229
And we should be able to
pick any two of these pairs

00:02:00.229 --> 00:02:01.990
in order to figure that out if we assume

00:02:01.990 --> 00:02:03.511
that this is indeed a line.

00:02:03.511 --> 00:02:07.713
Well, just for variety, let's
pick these middle two pairs.

00:02:07.713 --> 00:02:09.730
So what's our change in x?

00:02:09.730 --> 00:02:12.260
To go from one to five, we added four.

00:02:12.260 --> 00:02:13.730
And what's our change in y?

00:02:13.730 --> 00:02:16.920
To go from seven to 13, we added six.

00:02:16.920 --> 00:02:21.920
So our change in y is six
when our change in x is four.

00:02:22.770 --> 00:02:25.970
And I got the signs right,
in both case it's a positive.

00:02:25.970 --> 00:02:28.290
When x increases, y increased as well.

00:02:28.290 --> 00:02:29.560
So our slope is six fourths,

00:02:29.560 --> 00:02:31.250
and we could rewrite that if we like.

00:02:31.250 --> 00:02:33.040
Both six and four are divisible by two,

00:02:33.040 --> 00:02:35.280
so let be divide both the
numerator and the denominator

00:02:35.280 --> 00:02:38.143
by two and we get three
halves, and we're done.