1
00:00:00,000 --> 00:00:00,390


2
00:00:00,390 --> 00:00:08,870
We are asked to graph y is equal to 1/3x minus 2.

3
00:00:08,869 --> 00:00:11,739
Now, whenever you see an equation in this form, this is

4
00:00:11,740 --> 00:00:14,679
called slope-intercept form.

5
00:00:14,679 --> 00:00:21,289
And the general way of writing it is y is equal to mx plus b,

6
00:00:21,289 --> 00:00:23,140
where m is the slope.

7
00:00:23,140 --> 00:00:26,120
And here in this case, m is equal to 1/3-- so let me write

8
00:00:26,120 --> 00:00:31,300
that down-- m is equal to 1/3, and b is the y-intercept.

9
00:00:31,300 --> 00:00:35,310
So in this case, b is equal to negative 2.

10
00:00:35,310 --> 00:00:38,090
And you know that b is the y-intercept, because we know

11
00:00:38,090 --> 00:00:42,160
that the y-intercept occurs when x is equal to 0.

12
00:00:42,159 --> 00:00:45,229
So if x is equal to 0 in either of these situations,

13
00:00:45,229 --> 00:00:49,699
this term just becomes 0 and y will be equal to b.

14
00:00:49,700 --> 00:00:53,380
So that's what we mean by b is the y-intercept.

15
00:00:53,380 --> 00:00:55,690
So whenever you look at an equation in this form, it's

16
00:00:55,689 --> 00:00:57,169
actually fairly straightforward

17
00:00:57,170 --> 00:00:58,690
to graph this line.

18
00:00:58,689 --> 00:01:00,219
b is the y-intercept.

19
00:01:00,219 --> 00:01:04,090
In this case it is negative 2, so that means that this line

20
00:01:04,090 --> 00:01:09,810
must intersect the y-axis at y is equal to negative 2, so

21
00:01:09,810 --> 00:01:11,760
it's this point right here.

22
00:01:11,760 --> 00:01:15,910
Negative 1, negative 2, this is the point 0, negative 2.

23
00:01:15,909 --> 00:01:17,920
If you don't believe me, there's nothing magical about

24
00:01:17,920 --> 00:01:22,409
this, try evaluating or try solving for y when

25
00:01:22,409 --> 00:01:23,250
x is equal to 0.

26
00:01:23,250 --> 00:01:26,439
When x is equal to 0, this term cancels out and you're

27
00:01:26,439 --> 00:01:28,899
just left with y is equal to negative 2.

28
00:01:28,900 --> 00:01:31,510
So that's the y-intercept right there.

29
00:01:31,510 --> 00:01:35,830
Now, this 1/3 tells us the slope of the line.

30
00:01:35,829 --> 00:01:40,429
How much do we change in y for any change in x?

31
00:01:40,430 --> 00:01:43,760
So this tells us that 1/3, so that right

32
00:01:43,760 --> 00:01:46,230
there, is the slope.

33
00:01:46,230 --> 00:01:54,380
So it tells us that 1/3 is equal to the change in y over

34
00:01:54,379 --> 00:01:57,839
the change in x.

35
00:01:57,840 --> 00:02:01,760
Or another way to think about it, if x changes by 3, then y

36
00:02:01,760 --> 00:02:03,890
would change by 1.

37
00:02:03,890 --> 00:02:05,659
So let me graph that.

38
00:02:05,659 --> 00:02:08,930
So we know that this point is on the graph, that's the

39
00:02:08,930 --> 00:02:09,960
y-intercept.

40
00:02:09,960 --> 00:02:13,530
The slope tells us that if x changes by 3-- so let me go 3

41
00:02:13,530 --> 00:02:21,180
three to the right, 1, 2, 3-- that y will change by 1.

42
00:02:21,180 --> 00:02:23,819
So this must also be a point on the graph.

43
00:02:23,819 --> 00:02:24,719
And we could keep doing that.

44
00:02:24,719 --> 00:02:27,960
If x changes by 3, y changes by 1.

45
00:02:27,960 --> 00:02:34,030
If x goes down by 3, y will go down by 1.

46
00:02:34,030 --> 00:02:37,710
If x goes down by 6, y will go down by 2.

47
00:02:37,710 --> 00:02:43,599
It's that same ratio, so 1, 2, 3, 4, 5, 6, 1, 2.

48
00:02:43,599 --> 00:02:45,810
And you can see all of these points are on the line, and

49
00:02:45,810 --> 00:02:49,080
the line is the graph of this equation up here.

50
00:02:49,080 --> 00:02:51,690
So let me graph it.

51
00:02:51,689 --> 00:02:59,219
So it'll look something like that.

52
00:02:59,219 --> 00:03:00,810
And you're done.

53
00:03:00,810 --> 00:03:01,000