WEBVTT
1
00:00:03.390 --> 00:00:05.540 A:middle L:90%
All right, let's look at equations for the family
2
00:00:05.540 --> 00:00:07.650 A:middle L:90%
of linear functions that have a slope of to.
3
00:00:08.169 --> 00:00:11.000 A:middle L:90%
So we know that all equations of lines take on
4
00:00:11.000 --> 00:00:14.029 A:middle L:90%
the form y equals MX plus B if we want
5
00:00:14.029 --> 00:00:16.820 A:middle L:90%
to put them in slope Intercept form and M is
6
00:00:16.820 --> 00:00:20.039 A:middle L:90%
the slope. So we're saying that we have lines
7
00:00:20.039 --> 00:00:22.440 A:middle L:90%
that have a nem value of to a slope of
8
00:00:22.440 --> 00:00:25.449 A:middle L:90%
to so we could write equations of this form.
9
00:00:26.539 --> 00:00:30.829 A:middle L:90%
Y equals two x plus B B stands for the
10
00:00:30.829 --> 00:00:33.670 A:middle L:90%
Y intercept, and that's going to change depending on
11
00:00:33.670 --> 00:00:35.939 A:middle L:90%
the line. We don't have to use a be
12
00:00:35.939 --> 00:00:37.770 A:middle L:90%
there. We could use any letter. We want
13
00:00:37.939 --> 00:00:40.439 A:middle L:90%
to stand in for that. Why intercept now?
14
00:00:40.439 --> 00:00:42.399 A:middle L:90%
Let's take a look at the graphs of several of
15
00:00:42.399 --> 00:00:45.500 A:middle L:90%
these. So suppose we had y equals two x
16
00:00:45.500 --> 00:00:48.250 A:middle L:90%
plus zero. Just the line Y equals two X
17
00:00:48.640 --> 00:00:50.439 A:middle L:90%
. It would have a Y intercept of zero a
18
00:00:50.439 --> 00:00:53.549 A:middle L:90%
slope of to so it would look something like this
19
00:00:54.500 --> 00:00:56.320 A:middle L:90%
. Let's say we had y equals two x plus
20
00:00:56.320 --> 00:00:59.399 A:middle L:90%
one. It's going to be parallel to the line
21
00:00:59.399 --> 00:01:00.179 A:middle L:90%
. I just drew, and it has a Y
22
00:01:00.179 --> 00:01:07.599 A:middle L:90%
intercept of one same slope. Let's look at y
23
00:01:07.599 --> 00:01:11.079 A:middle L:90%
equals two X minus one. It has a Y
24
00:01:11.079 --> 00:01:14.900 A:middle L:90%
intercept of negative one same slope. So it's going
25
00:01:14.900 --> 00:01:17.819 A:middle L:90%
to be parallel that didn't live to parallel. We'll
26
00:01:17.819 --> 00:01:29.250 A:middle L:90%
try that again one more time. Okay, There
27
00:01:29.250 --> 00:01:32.260 A:middle L:90%
we go. Now for part B. We want
28
00:01:32.260 --> 00:01:34.760 A:middle L:90%
an equation for the family of functions that all go
29
00:01:34.760 --> 00:01:38.120 A:middle L:90%
through the point to one. Basically, when you
30
00:01:38.120 --> 00:01:40.140 A:middle L:90%
see f of two equals one, that means the
31
00:01:40.140 --> 00:01:42.230 A:middle L:90%
point to one. So if we take our point
32
00:01:42.230 --> 00:01:46.450 A:middle L:90%
slope form, which is why minus y one equals
33
00:01:46.459 --> 00:01:49.510 A:middle L:90%
m times X minus X one. And if we
34
00:01:49.510 --> 00:01:52.390 A:middle L:90%
substitute the point to one in for X one and
35
00:01:52.390 --> 00:01:55.310 A:middle L:90%
why one we'll get an equation that looks like this
36
00:01:55.739 --> 00:01:59.090 A:middle L:90%
. Why minus one equals m times a quantity X
37
00:01:59.090 --> 00:02:01.959 A:middle L:90%
minus two. So this represents the family of functions
38
00:02:01.959 --> 00:02:05.390 A:middle L:90%
that all go through the point to one. Now
39
00:02:05.390 --> 00:02:07.310 A:middle L:90%
, if we want to change that into slope intercept
40
00:02:07.310 --> 00:02:09.150 A:middle L:90%
form, we could go ahead and distribute the M
41
00:02:13.039 --> 00:02:14.919 A:middle L:90%
, and then we could add one to both sides
42
00:02:14.930 --> 00:02:16.189 A:middle L:90%
. But I think it's more informational if we leave
43
00:02:16.189 --> 00:02:23.689 A:middle L:90%
it the other way. All right, let's sketch
44
00:02:23.689 --> 00:02:28.319 A:middle L:90%
several of these graphs, so we want point.
45
00:02:28.330 --> 00:02:30.849 A:middle L:90%
We went lines that go through the point to one
46
00:02:37.280 --> 00:02:38.409 A:middle L:90%
. So we locate the point to one and then
47
00:02:38.409 --> 00:02:40.009 A:middle L:90%
we just draw a whole bunch of lines that go
48
00:02:40.009 --> 00:02:43.699 A:middle L:90%
through that point. We could have this line.
49
00:02:44.740 --> 00:02:47.180 A:middle L:90%
We could have this line. We could have this
50
00:02:47.180 --> 00:02:51.750 A:middle L:90%
line. We could have this line. There's infinitely
51
00:02:51.750 --> 00:02:55.069 A:middle L:90%
many possibilities. Lastly, we're going to combine both
52
00:02:55.069 --> 00:02:58.939 A:middle L:90%
parts, so we want the function that has a
53
00:02:58.939 --> 00:03:00.639 A:middle L:90%
slope of two and goes through the point to one
54
00:03:00.949 --> 00:03:02.909 A:middle L:90%
. So let's go back to that point slope form
55
00:03:02.909 --> 00:03:06.569 A:middle L:90%
again. Why? Minus y one equals M times
56
00:03:06.569 --> 00:03:08.889 A:middle L:90%
X minus X one. And let's substitute the point
57
00:03:08.889 --> 00:03:13.020 A:middle L:90%
to one. And they're So why minus one equals
58
00:03:13.030 --> 00:03:15.090 A:middle L:90%
? We're also going to substitute the slope of two
59
00:03:15.090 --> 00:03:17.289 A:middle L:90%
in there. So why minus one equals two times
60
00:03:17.289 --> 00:03:21.039 A:middle L:90%
the quantity X minus two. Now, this is
61
00:03:21.039 --> 00:03:22.610 A:middle L:90%
the equation of the line. We could leave it
62
00:03:22.610 --> 00:03:23.669 A:middle L:90%
like that, or we could change it to slope
63
00:03:23.669 --> 00:03:29.789 A:middle L:90%
intercept form first by distributing the to and then by
64
00:03:29.789 --> 00:03:31.250 A:middle L:90%
adding one to both sides. 12 y equals two
65
00:03:31.250 --> 00:03:32.150 A:middle L:90%
x minus three