WEBVTT

1
00:00:00.256 --> 00:00:02.560
Welcome to Brainfuse.

2
00:00:03.840 --> 00:00:10.579
In this lesson, we are going to find the equation of a slope. And our sample problem asks us to do that

3
00:00:10.579 --> 00:00:16.384
and a little bit extra, just so we understand how all parts of the linear equation are related.

4
00:00:16.640 --> 00:00:22.784
So here it is: find the slope of the line 2x + 4 y equals 8

5
00:00:23.040 --> 00:00:29.184
And then find its x- and y-intercepts. When graphing a line, it's helpful to write the equation in

6
00:00:29.440 --> 00:00:31.488
Slope intercept form.

7
00:00:31.744 --> 00:00:33.255
And that is:

8
00:00:33.255 --> 00:00:38.400
y equals mx plus b

9
00:00:38.400 --> 00:00:38.400


10
00:00:38.656 --> 00:00:40.448
And in this case

11
00:00:40.704 --> 00:00:44.032
the m stands for the slope

12
00:00:45.056 --> 00:00:48.640
The b stands for the y-intercept

13
00:00:53.248 --> 00:00:57.088
and X & Y would be the coordinates at any point on a line

14
00:00:57.600 --> 00:01:01.184
So as you can see this already gives us part of the answer.

15
00:01:01.440 --> 00:01:07.328
The b represents the y-intercept, and that's one of the values we need to look for

16
00:01:07.584 --> 00:01:13.728
Okay so this equation is not in slope intercept form and we need to get it

17
00:01:13.984 --> 00:01:23.180
We need to get it there so let's work on that. We have 2x plus 4y equals 8.

18
00:01:23.200 --> 00:01:27.296
We will keep the Y on the left and we'll move that 2X

19
00:01:27.808 --> 00:01:30.880
So subtract 2x from both sides

20
00:01:32.416 --> 00:01:34.976
And that gives us

21
00:01:35.744 --> 00:01:36.768
4y

22
00:01:37.024 --> 00:01:38.304
Equals

23
00:01:38.560 --> 00:01:40.352
8 minus 2x

24
00:01:41.632 --> 00:01:45.472
And now I need to isolate that y, so divide 4

25
00:01:48.544 --> 00:01:50.080
On both sides

26
00:01:50.336 --> 00:01:53.920
And we have 8/4

27
00:01:54.176 --> 00:01:56.736
Is equal to 2

28
00:01:56.992 --> 00:02:03.136
And 2 divided by 4 is equal to one half so we have two minus 1/2 x

29
00:02:03.392 --> 00:02:06.720
And notice that the coefficient

30
00:02:06.976 --> 00:02:13.120
In front of an x would be the slope, so just to make these aligned let's put the slope first

31
00:02:13.376 --> 00:02:14.400
So we have y

32
00:02:14.656 --> 00:02:16.960
Equals -1/2

33
00:02:17.472 --> 00:02:18.496
x

34
00:02:18.752 --> 00:02:22.080
And this is a positive 2, so we have plus

35
00:02:22.336 --> 00:02:23.104
2.

36
00:02:24.384 --> 00:02:30.528
And that is our equation in slope intercept form . We can work with this equation much

37
00:02:30.784 --> 00:02:35.136
more easily. So this already shows us the slope and the y-intercept

38
00:02:35.392 --> 00:02:37.184
Our slope we see

39
00:02:37.440 --> 00:02:39.488
Is -1/2

40
00:02:45.632 --> 00:02:48.192
and our y-intercept

41
00:02:48.704 --> 00:02:52.800
would be 2. And at that point that is when

42
00:02:54.080 --> 00:02:59.374
if this were our coordinate system

43
00:03:00.992 --> 00:03:04.832
This line would cross the y-axis at 2

44
00:03:05.344 --> 00:03:08.160
At the point where the line crosses the y axis

45
00:03:08.416 --> 00:03:09.952
x is equal to

46
00:03:10.208 --> 00:03:11.232
Zero

47
00:03:11.488 --> 00:03:16.096
So we write it out in alphabetical order: x first, 0

48
00:03:16.352 --> 00:03:21.216
and y second, 2. So our y-intercept

49
00:03:21.472 --> 00:03:26.080
put y-int, equals 0, 2

50
00:03:27.104 --> 00:03:31.456
Okay, so now we have to find the x-intercept

51
00:03:31.712 --> 00:03:37.856
So what we can do is set y equal to 0 and then solve for x.

52
00:03:38.112 --> 00:03:41.184
Because, just as we saw here, when

53
00:03:41.440 --> 00:03:46.048
our line crosses the y-axis: x has to be equal to 0.

54
00:03:46.304 --> 00:03:48.096
When a line crosses any point

55
00:03:48.352 --> 00:03:52.704
On the x-axis, y is equal to 0.

56
00:03:52.960 --> 00:03:54.240
So

57
00:03:58.872 --> 00:04:00.889
I'll just divide these

58
00:04:06.528 --> 00:04:08.576
So that give us: 0 equals

59
00:04:08.832 --> 00:04:10.112
-1/2

60
00:04:10.368 --> 00:04:11.904
x plus

61
00:04:12.160 --> 00:04:16.767
2. So I'll subtract both sides by 2

62
00:04:19.072 --> 00:04:24.567
That gives us -2 equals -1/2 x

63
00:04:24.567 --> 00:04:30.080
We need to isolate that x, so let's multiply both sides by -2.

64
00:04:35.968 --> 00:04:38.272
Okay so

65
00:04:38.528 --> 00:04:44.075
That cancels the 2 and the negative out leaving us with one x,

66
00:04:44.075 --> 00:04:47.232
and -2 times -2 is equal to 4.

67
00:04:47.488 --> 00:04:53.376
So positive 4 is X and the coordinates for that point would then be

68
00:04:53.632 --> 00:04:54.656
4

69
00:04:55.168 --> 00:04:55.936
0

70
00:04:56.192 --> 00:05:02.336
Because y is 0 anytime a line crosses the x-intercept

71
00:05:08.992 --> 00:05:15.136
So that is one strategy you can use to solve these problems, and I'm going to clear the work on the

72
00:05:15.392 --> 00:05:19.744
bottom so that we can use another approach to solve these problems.

73
00:05:31.008 --> 00:05:35.872
So let just use this answer to see if we can figure out the slope of this line.

74
00:05:37.920 --> 00:05:41.504
Okay, so there we had the x-intercept, 4 and 0

75
00:05:41.760 --> 00:05:43.296
And the y-intercept

76
00:05:43.552 --> 00:05:44.832
0 and 2

77
00:05:47.648 --> 00:05:52.512
So the slope is calculated as the change in y values

78
00:05:55.840 --> 00:05:57.632
The triangle represents change

79
00:05:58.144 --> 00:05:59.936
Change in y values

80
00:06:01.728 --> 00:06:02.496
Over

81
00:06:02.752 --> 00:06:06.592
The change in x values. You may also have learned it

82
00:06:06.848 --> 00:06:11.816
as rise over run

83
00:06:12.098 --> 00:06:14.371
Where rise is

84
00:06:15.552 --> 00:06:16.320
Vertical

85
00:06:17.088 --> 00:06:17.856
and run

86
00:06:18.880 --> 00:06:19.904


87
00:06:20.416 --> 00:06:21.184
And run

88
00:06:21.952 --> 00:06:24.000
Runs horizontally along

89
00:06:24.512 --> 00:06:25.792
A grid

90
00:06:27.072 --> 00:06:31.680
So in this, case we have the change in y over change in x. So change in y:

91
00:06:32.192 --> 00:06:33.728
We have 2

92
00:06:33.984 --> 00:06:35.008
and 0

93
00:06:36.032 --> 00:06:36.800
As

94
00:06:37.312 --> 00:06:40.640
The two points so 2 minus 0

95
00:06:41.399 --> 00:06:46.016
And we have 0

96
00:06:46.272 --> 00:06:47.040
and 4

97
00:06:47.552 --> 00:06:49.600
That's over 0 minus 4

98
00:06:53.696 --> 00:06:55.744
Okay, and that is equal to

99
00:06:56.000 --> 00:06:57.847
this would be 2 and this is

100
00:06:57.847 --> 00:07:03.168
-4. So -2/4 simplifies to negative

101
00:07:03.168 --> 00:07:05.472
1/2 and again that is our slope

102
00:07:05.728 --> 00:07:11.872
Okay, just to be sure, it does not matter which order you subtract these values, as long as your subtracting a y

103
00:07:12.128 --> 00:07:13.920
from a Y, and an x from an x.

104
00:07:14.176 --> 00:07:17.504
So just for instance, 0 minus 2

105
00:07:18.784 --> 00:07:21.344
If we did it the other way, 0 minus 2

106
00:07:23.136 --> 00:07:24.416
Over

107
00:07:26.208 --> 00:07:27.488
4 minus 0

108
00:07:30.816 --> 00:07:32.864
Is also equal to

109
00:07:33.120 --> 00:07:35.168
-2 over 4

110
00:07:36.960 --> 00:07:38.496
So you don't have to worry about that

111
00:07:39.264 --> 00:07:45.408
You'll see both kinds of problems in the practice set and can use the slope intercept equation to find

112
00:07:45.664 --> 00:07:51.808
values of x-intercepts and y-intercepts or this rise over run formula to find the slope. And thank you for wathcing this lesson.