1
00:00:00;00 --> 00:00:03;03
Zero to one, there was
none. From one to two, y

2
00:00:03;04 --> 00:00:11;12
changed by .5 as much. Then
from 2 to 3, y changed by

3
00:00:11;13 --> 00:00:15;10
1, so we set that one up
to then

4
00:00:15;11 --> 00:00:18;09
[It's one point five.]

5
00:00:18;10 --> 00:00:19;10
One and a half, thank you.

6
00:00:19;11 --> 00:00:31;09
what did you guys get for
this next step?

7
00:00:31;10 --> 00:00:33;04
From 3 to 4, how much does
y change?

8
00:00:33;05 --> 00:00:38;00
[one point five.]

9
00:00:38;01 --> 00:00:41;02
By one and a half times as
much. So if I was already

10
00:00:41;03 --> 00:00:43;12
at one and a half and y is
going to change by another

11
00:00:43;13 --> 00:00:45;04
one and a half, where I am
going to be?

12
00:00:45;05 --> 00:00:45;14
[Three.]

13
00:00:45;15 --> 00:00:50;03
Three? Okay. so this side,
like I said, I was walking

14
00:00:50;04 --> 00:00:52;11
around and you guys were
fine. Come over to the

15
00:00:52;12 --> 00:01:03;04
negatives with me. Up
here, x changes by negative

16
00:01:03;05 --> 00:01:06;03
one. Rate of change
corresponding in that

17
00:01:06;04 --> 00:01:11;11
interval is...negative
half. So, what does that

18
00:01:11;12 --> 00:01:15;12
mean? As x changes from
zero to negative one, y

19
00:01:15;13 --> 00:01:23;14
changes how? Negative half.
Finish the sentence. Times

20
00:01:23;15 --> 00:01:31;07
as much. where am I going
to put this next dot? As x

21
00:01:31;08 --> 00:01:33;11
changes from zero to
negative one, y changes

22
00:01:33;12 --> 00:01:38;04
negative point five times
as much. So what's negative

23
00:01:38;05 --> 00:01:40;07
point five times as much as
negative one?

24
00:01:40;08 --> 00:01:45;08
Positive point five.

25
00:01:45;09 --> 00:01:53;11
Who had the point coming
down here? Raise your hand.

26
00:01:53;12 --> 00:02:00;11
The reason, ladies and
gents, is because you just

27
00:02:00;12 --> 00:02:05;04
looked at the fact that it
was negative point five and

28
00:02:05;05 --> 00:02:08;02
said I'm going to go down
point five because it was

29
00:02:08;03 --> 00:02:13;00
negative point five. Rates
of change, you guys know

30
00:02:13;01 --> 00:02:16;11
this, depend on how x
changes as well. If x

31
00:02:16;12 --> 00:02:21;04
changed by negative one and
the rate of change is

32
00:02:21;05 --> 00:02:24;03
negative half then y
changes negative half as

33
00:02:24;04 --> 00:02:27;00
much and it'll turn
positive as you saw. You've

34
00:02:27;01 --> 00:02:31;01
gotta think about these
things. You all had your

35
00:02:31;02 --> 00:02:38;05
graph going this way. Then
what? As x changes from

36
00:02:38;06 --> 00:02:40;05
negative one to negative
two, what's the rate of

37
00:02:40;06 --> 00:02:46;08
change? Well, negative one
to negative two, in that

38
00:02:46;09 --> 00:02:51;00
interval,the rate of change
is negative one. Again,

39
00:02:51;01 --> 00:02:54;09
the change of x in this
interval is how much?

40
00:02:54;10 --> 00:02:56;13
[Negative one.]

41
00:02:56;14 --> 00:03:00;11
Negative one. The rate of
change is negative one as

42
00:03:00;12 --> 00:03:04:02
well. If x changed by
negative one, y will change

43
00:03:04;03 --> 00:03:08;02
by how much? Negative one
times as much,

44
00:03:08;03 --> 00:03:13;05
meaning what? Positive one.
Danielle?

45
00:03:13;06 --> 00:03:16;03
[Do you times it so then
its the negative...]

46
00:03:16;04 --> 00:03:22;02
That's how it ends up
working, exactly. That

47
00:03:22;03 --> 00:03:24;09
whole thing that I drilled
into you back in the day,

48
00:03:24;10 --> 00:03:29;09
of rate of change is this
many times as much as your

49
00:03:29;10 --> 00:03:34;01
x change, that's what you just said, Danielle.