1
00:00:00,000 --> 00:00:00,490


2
00:00:00,490 --> 00:00:03,480
We have three lines and we have to figure out which of

3
00:00:03,480 --> 00:00:05,209
the three are parallel.

4
00:00:05,209 --> 00:00:08,250
So line A-- and it can't be parallel on its own, it has to

5
00:00:08,250 --> 00:00:10,509
be parallel to another of the three lines.

6
00:00:10,509 --> 00:00:13,740
So the equation for line A is y is equal

7
00:00:13,740 --> 00:00:19,079
to 3/4 x minus four.

8
00:00:19,079 --> 00:00:29,939
Line B is 4y minus 20 is equal to negative 3x.

9
00:00:29,940 --> 00:00:38,579
And then line C is negative 3x plus 4y is equal to 40.

10
00:00:38,579 --> 00:00:41,089
So to figure out if any of these lines are parallel to

11
00:00:41,090 --> 00:00:42,450
any of the other lines, we just have to

12
00:00:42,450 --> 00:00:45,210
compare their slopes.

13
00:00:45,210 --> 00:00:47,420
If any two of these lines have the same slope and they're

14
00:00:47,420 --> 00:00:50,109
different lines, they have different y-intercepts, then

15
00:00:50,109 --> 00:00:51,909
they're going to be parallel.

16
00:00:51,909 --> 00:00:53,969
Now line A, it's very easy to figure out its slope.

17
00:00:53,969 --> 00:00:55,979
It's already in slope-intercept form.

18
00:00:55,979 --> 00:01:02,909
This is mx plus b, the slope is 3/4 and the y-intercept,

19
00:01:02,909 --> 00:01:04,879
which isn't as relevant when you're figuring out parallel

20
00:01:04,879 --> 00:01:07,189
lines, is negative 4.

21
00:01:07,189 --> 00:01:10,179
So let's see what the other character's slopes are.

22
00:01:10,180 --> 00:01:12,180
This isn't in any kind of standard form.

23
00:01:12,180 --> 00:01:14,100
It's not a standard form, slope-intercept, or

24
00:01:14,099 --> 00:01:16,379
point-slope form, but let's see what the slope

25
00:01:16,379 --> 00:01:17,299
of this line is.

26
00:01:17,299 --> 00:01:19,899
So to get it into slope-intercept form, which is

27
00:01:19,900 --> 00:01:23,050
really the easiest one to pick out the slope from, let's add

28
00:01:23,049 --> 00:01:24,534
20 to both sides of this equation.

29
00:01:24,534 --> 00:01:28,799


30
00:01:28,799 --> 00:01:31,239
The left-hand side, those cancel out, that was the whole

31
00:01:31,239 --> 00:01:37,649
point, you get 4y is equal to negative 3x plus 20.

32
00:01:37,650 --> 00:01:39,670
And now we can divide everything by 4.

33
00:01:39,670 --> 00:01:44,769


34
00:01:44,769 --> 00:01:53,519
We are left with y is equal to negative 3/4 x plus 5.

35
00:01:53,519 --> 00:01:56,129
So in this case, y-intercept is 5, but most importantly,

36
00:01:56,129 --> 00:02:01,329
the slope is negative 3/4, so it's different than this guy.

37
00:02:01,329 --> 00:02:04,090
This is negative 3/4, this is positive 3/4, so these two

38
00:02:04,090 --> 00:02:06,359
guys definitely aren't parallel.

39
00:02:06,359 --> 00:02:09,310
Let's move on of this guy in standard form.

40
00:02:09,310 --> 00:02:11,250
So let's get the x term on the other side.

41
00:02:11,250 --> 00:02:13,729
So let's add 3x to both sides of this equation.

42
00:02:13,729 --> 00:02:17,590


43
00:02:17,590 --> 00:02:19,129
Left-hand side, these cancel out.

44
00:02:19,129 --> 00:02:24,799
We're just left with 4y is equal to 3x plus 40, or 40

45
00:02:24,800 --> 00:02:26,620
plus 3x, either way.

46
00:02:26,620 --> 00:02:29,819
Now we can divide both sides by 4 you have to divide

47
00:02:29,819 --> 00:02:31,979
every term by 4.

48
00:02:31,979 --> 00:02:34,449
The left-hand side, you're left with y.

49
00:02:34,449 --> 00:02:39,719
The right-hand side, you have 3/4 x plus 10.

50
00:02:39,719 --> 00:02:44,599
So here, our slope is 3/4 and our y-intercept, if we care

51
00:02:44,599 --> 00:02:46,239
about it, is 10.

52
00:02:46,240 --> 00:02:50,590
So this line and this line have the exact same slope,

53
00:02:50,590 --> 00:02:52,560
3/4, and they're different lines because their

54
00:02:52,560 --> 00:02:54,280
y-intercept is different.

55
00:02:54,280 --> 00:02:58,479
So we know that A and C are parallel lines and B is not

56
00:02:58,479 --> 00:03:02,219
parallel to either one of the other two.

57
00:03:02,219 --> 00:03:02,665