1
00:00:00,000 --> 00:00:00,720


2
00:00:00,720 --> 00:00:03,690
Deirdre is working with a function that contains the

3
00:00:03,690 --> 00:00:05,060
following points.

4
00:00:05,059 --> 00:00:07,349
These are the x values, these are y values.

5
00:00:07,349 --> 00:00:12,460
They ask us, is this function linear or non-linear?

6
00:00:12,460 --> 00:00:16,379
So linear functions, the way to tell them is for any given

7
00:00:16,379 --> 00:00:19,609
change in x, is the change in y always going

8
00:00:19,609 --> 00:00:20,759
to be the same value.

9
00:00:20,760 --> 00:00:26,179
For example, for any one-step change in x, is the change in

10
00:00:26,179 --> 00:00:27,460
y always going to be 3?

11
00:00:27,460 --> 00:00:28,940
Is it always going to be 5?

12
00:00:28,940 --> 00:00:31,450
If it's always going to be the same value, you're dealing

13
00:00:31,449 --> 00:00:32,670
with a linear function.

14
00:00:32,670 --> 00:00:36,570
If for each change in x--so over here x is always changing

15
00:00:36,570 --> 00:00:40,380
by 1, so since x is always changing by 1, the change in

16
00:00:40,380 --> 00:00:42,800
y's have to always be the same.

17
00:00:42,799 --> 00:00:43,919
If they're not, then we're dealing with

18
00:00:43,920 --> 00:00:45,200
a non-linear function.

19
00:00:45,200 --> 00:00:47,280
We can actually show that plotting out.

20
00:00:47,280 --> 00:00:50,149
If the changes in x-- we're going by different values, if

21
00:00:50,149 --> 00:00:53,189
this went from 1 to 2 and then 2 to 4-- what you'd want to

22
00:00:53,189 --> 00:00:57,309
do, then, is divide the change in y by the change in x, and

23
00:00:57,310 --> 00:00:59,030
that should always be a constant.

24
00:00:59,030 --> 00:01:00,280
In fact, let me write that down.

25
00:01:00,280 --> 00:01:03,579


26
00:01:03,579 --> 00:01:11,659
If something is linear, then the change in y over the

27
00:01:11,659 --> 00:01:17,239
change in x always constant.

28
00:01:17,239 --> 00:01:21,759


29
00:01:21,760 --> 00:01:23,960
Now, in this example, the change in x's

30
00:01:23,959 --> 00:01:25,479
are always 1, right?

31
00:01:25,480 --> 00:01:28,890
We go from 1 to 2, 2 to 3, 3 to 4, 4 to 5.

32
00:01:28,890 --> 00:01:34,060
So in this example, the change in x is always going to be 1.

33
00:01:34,060 --> 00:01:38,030
So in order for this function to be linear, our change in y

34
00:01:38,030 --> 00:01:40,180
needs to be constant because we're just going to take that

35
00:01:40,180 --> 00:01:41,310
and divide it by 1.

36
00:01:41,310 --> 00:01:43,909
So let's see if our change in y is constant.

37
00:01:43,909 --> 00:01:48,479
When we go from 11 to 14, we go up by 3.

38
00:01:48,480 --> 00:01:51,500
When we go from 14 to 19, we go up by 5, so I already see

39
00:01:51,500 --> 00:01:52,980
that it is not constant.

40
00:01:52,980 --> 00:01:55,189
We didn't go up by 3 this time, we went up by 5.

41
00:01:55,189 --> 00:01:58,099
And here, we go up by 7.

42
00:01:58,099 --> 00:02:01,229
And here, we're going up by 9.

43
00:02:01,230 --> 00:02:04,780
So we're actually going up by increasing amounts, so we're

44
00:02:04,780 --> 00:02:08,379
definitely dealing with a non-linear function.

45
00:02:08,379 --> 00:02:10,780
And we can see that if we graph it out.

46
00:02:10,780 --> 00:02:13,390
So let me draw-- I'll do a rough graph here.

47
00:02:13,389 --> 00:02:17,409
So let me make that my vertical axis, my y-axis.

48
00:02:17,409 --> 00:02:19,509
And we go all the way up to 35.

49
00:02:19,509 --> 00:02:26,039
So I'll just do 10, 20, 30.

50
00:02:26,039 --> 00:02:29,469
Actually, I can it do a little bit more granularly than that.

51
00:02:29,469 --> 00:02:44,650
I could do 5, 10, 15, 20, 25, 30, and then 35.

52
00:02:44,650 --> 00:02:46,689
And then our values go 1 through 5.

53
00:02:46,689 --> 00:02:48,969
I'll do it on this axis right here.

54
00:02:48,969 --> 00:02:52,009
They're not obviously the exact same scale, so I'll do

55
00:02:52,009 --> 00:02:58,030
1, 2, 3, 4, and 5.

56
00:02:58,030 --> 00:02:59,610
So let's plot these points.

57
00:02:59,610 --> 00:03:03,800
So the first point is 1, 11, when x is 1, y is 11.

58
00:03:03,800 --> 00:03:04,760
This is our x-axis.

59
00:03:04,759 --> 00:03:08,599
When x is 1, y is 11, that's right about there.

60
00:03:08,599 --> 00:03:15,159
When x is 2, y is 14, that's right about there.

61
00:03:15,159 --> 00:03:23,569
When x is 3, y is 19, right about there.

62
00:03:23,569 --> 00:03:32,199
When x is 4, y is 26, right about there.

63
00:03:32,199 --> 00:03:40,079
And then finally, when x is 5, y is 35, right up there.

64
00:03:40,080 --> 00:03:41,810
So you can immediately see that this is not

65
00:03:41,810 --> 00:03:44,479
tracing out a line.

66
00:03:44,479 --> 00:03:49,109
If this was a linear function, then all the points would be

67
00:03:49,110 --> 00:03:51,250
on a line that looks something like that.

68
00:03:51,250 --> 00:03:53,530
That's why it's called a linear function.

69
00:03:53,530 --> 00:03:56,150
In this case, it's not, it's non-linear.

70
00:03:56,150 --> 00:03:59,319
The rate of increase as x changes is going up.

71
00:03:59,319 --> 00:04:00,733