1 00:00:01,010 --> 00:00:08,120 Students so far, we have seen these two ways in which we represent a straight line right now, let's 2 00:00:08,120 --> 00:00:12,470 learn the third way in which we represent a straight line in this video. 3 00:00:12,820 --> 00:00:18,530 So that would be why is equal to M. X plus C now M is the slope. 4 00:00:19,690 --> 00:00:26,260 And we learned what we mean with the slope soon and C stands for the Y intercept, which is the value 5 00:00:26,260 --> 00:00:27,970 when X is equal to zero. 6 00:00:28,330 --> 00:00:32,340 All right, let's try to understand this equation in a better manner. 7 00:00:35,000 --> 00:00:39,980 OK, so for that, first, we need to understand what do we mean with the slope of a line? 8 00:00:40,370 --> 00:00:46,570 All right, let's try to understand that now over here I have a line and let me have another line over 9 00:00:46,580 --> 00:00:49,360 here that goes like this right now over here. 10 00:00:49,400 --> 00:00:51,940 The angle is three to one, right. 11 00:00:51,950 --> 00:00:53,420 And this angle is the tattoo. 12 00:00:53,750 --> 00:00:56,720 Now, this line has a negative slope. 13 00:00:57,230 --> 00:00:58,430 What do we mean with that? 14 00:00:58,730 --> 00:01:00,530 It's a decreasing function. 15 00:01:00,710 --> 00:01:05,810 As the X increases, you can see that the Y value keeps on decreasing. 16 00:01:05,880 --> 00:01:08,450 Right over here, you have a positive slope. 17 00:01:08,660 --> 00:01:14,300 That is as the value of X increases, the value of Y keeps increasing. 18 00:01:14,480 --> 00:01:21,710 So this over here is a decreasing function and this over here is an increasing function. 19 00:01:22,070 --> 00:01:22,530 All right. 20 00:01:22,790 --> 00:01:25,910 So over here we have defined the angles. 21 00:01:25,920 --> 00:01:27,530 This is angle to one. 22 00:01:27,740 --> 00:01:28,880 This is theta two. 23 00:01:29,060 --> 00:01:32,180 Now, the slope is obtained by finding Tante to. 24 00:01:34,060 --> 00:01:40,120 All right, now, when you find the slope, you will find that in this case, Santita one will give 25 00:01:40,120 --> 00:01:41,400 you a negative value. 26 00:01:41,530 --> 00:01:45,150 And remember, you can see more about an internal metric. 27 00:01:45,460 --> 00:01:49,930 Now, over here you will get to which is a positive value. 28 00:01:50,440 --> 00:01:56,260 Now, remember, these type of angles which are taken in this way are called a positive angle. 29 00:01:56,380 --> 00:01:57,760 And this is a negative angle. 30 00:01:57,910 --> 00:02:00,390 But typically that's not required in questions. 31 00:02:00,400 --> 00:02:02,660 But again, this is a negative angle. 32 00:02:02,680 --> 00:02:03,910 This is a positive angle. 33 00:02:04,090 --> 00:02:04,800 That's right. 34 00:02:04,800 --> 00:02:07,290 Down of this angle will give you a positive value. 35 00:02:07,540 --> 00:02:08,970 And this is a negative angle. 36 00:02:08,980 --> 00:02:13,630 That's why down of this angle will give you a negative value, but in a visual manner. 37 00:02:13,630 --> 00:02:16,000 We can understand it like this over here. 38 00:02:16,120 --> 00:02:18,670 As X increases, Y decreases. 39 00:02:18,670 --> 00:02:18,890 Right. 40 00:02:18,910 --> 00:02:21,180 Because these values of light are negative. 41 00:02:21,400 --> 00:02:26,170 So it's a decreasing function and hence the slope is negative all year. 42 00:02:26,170 --> 00:02:34,480 As X increases, Y increases right at point for X equals four, you have Y, it is around to right at 43 00:02:34,540 --> 00:02:38,260 point five, X equals five, you'll have Y around four. 44 00:02:38,270 --> 00:02:43,360 So you can see that it's an increasing function and hence it has a positive slope. 45 00:02:43,630 --> 00:02:50,230 Now remember, slope is given by fan of Peter already having identified this. 46 00:02:50,380 --> 00:02:52,090 Let's get back to our equation. 47 00:02:52,270 --> 00:02:59,260 We have seen that slope describes this land of the line and we have seen that it's given by 10 of the 48 00:02:59,260 --> 00:03:07,060 top right slope is given by 2010, where Theta is the angle that the line makes with the x axis. 49 00:03:07,330 --> 00:03:07,810 All right. 50 00:03:07,990 --> 00:03:10,590 Now, let's take an example of an equation of a line. 51 00:03:10,750 --> 00:03:13,510 You have three Y is equal to twelve minus for X. 52 00:03:13,900 --> 00:03:14,470 All right. 53 00:03:14,770 --> 00:03:18,190 Now, over here, I can say that Y is equal to. 54 00:03:19,140 --> 00:03:23,890 Minus four by three X, plus 12 by three, which is equal to or right. 55 00:03:24,090 --> 00:03:25,140 It's the same equation. 56 00:03:25,270 --> 00:03:32,340 I just divide this by three and I divide this side also by three by half way over here and all I have 57 00:03:32,340 --> 00:03:33,020 12 by three. 58 00:03:33,030 --> 00:03:35,530 That's four and minus four by three X. 59 00:03:35,560 --> 00:03:37,070 That's what we have over here. 60 00:03:37,440 --> 00:03:37,910 All right. 61 00:03:38,100 --> 00:03:44,940 Now, if you have an equation like this compared with this form over here, you can see that minus four 62 00:03:44,940 --> 00:03:49,180 by three is the slope and four is the Y intercept. 63 00:03:49,470 --> 00:03:53,270 And what do we mean when we say that minus four by three is the slope? 64 00:03:53,760 --> 00:03:56,400 It means it describes the end of the line. 65 00:03:56,610 --> 00:04:01,470 And also it means that 20 to one is equal to minus four by three. 66 00:04:01,920 --> 00:04:02,360 All right. 67 00:04:02,610 --> 00:04:08,940 So we have seen the third way in which a line is described, which is why is equal to and makes policy. 68 00:04:09,030 --> 00:04:09,370 Right. 69 00:04:09,630 --> 00:04:13,870 And over here, M is the slope and C is the Y intercept. 70 00:04:14,080 --> 00:04:15,620 Now, let me take that over here. 71 00:04:16,750 --> 00:04:22,980 Now, over here, we have seen this interesting form weather wise of the form and makes policy. 72 00:04:22,990 --> 00:04:28,000 Right now we are going to see the two point form of writing a line. 73 00:04:28,300 --> 00:04:34,510 And along with this, we will learn a little bit more about the slope that is we have seen before that 74 00:04:34,510 --> 00:04:41,030 the slope is Dante right now, or you will see another way in which we can identify the slope already 75 00:04:41,200 --> 00:04:41,680 or here. 76 00:04:41,680 --> 00:04:42,610 I have two points. 77 00:04:42,880 --> 00:04:46,300 Let me tell them as x1 why one and x2 y2. 78 00:04:46,480 --> 00:04:48,190 But these are these two points. 79 00:04:48,390 --> 00:04:57,640 Now I can write the equation of this line as Y minus Y one by X, minus X one where you take any point 80 00:04:57,640 --> 00:05:03,810 as the first point is equal to Y to minus Y one by x2 minus x1. 81 00:05:04,240 --> 00:05:10,120 And remember any point can be taken as the first point and any point can be taken as the second point. 82 00:05:10,570 --> 00:05:15,010 All right, let's try to apply this equation in a real case. 83 00:05:15,260 --> 00:05:19,360 Let this point be zero four and this point B three zero. 84 00:05:19,750 --> 00:05:26,740 When we applied over here we get Y minus four divided by X, minus zero is equal to zero, minus four 85 00:05:26,920 --> 00:05:28,320 by three minus zero. 86 00:05:28,450 --> 00:05:28,830 Right. 87 00:05:29,020 --> 00:05:30,970 So that gives us Y minus four. 88 00:05:31,150 --> 00:05:35,050 Divided by X is equal to minus four by three. 89 00:05:35,320 --> 00:05:42,040 Now if you take X over here and you take this minus four also to this side, this becomes Y minus four 90 00:05:42,040 --> 00:05:48,300 by Y is equal to minus four by three X plus four, which is the same equation which we had over here. 91 00:05:48,610 --> 00:05:48,960 Right. 92 00:05:49,210 --> 00:05:52,960 So this is called the two point four of often line. 93 00:05:53,110 --> 00:05:56,220 So to write this equation, you need two points. 94 00:05:56,230 --> 00:05:57,860 That's why it's called a two point four. 95 00:05:58,180 --> 00:06:05,530 Now, an interesting point to note over here is this part over here that is Y to minus Y by X to minus 96 00:06:05,530 --> 00:06:07,770 X, one is the slope of the line. 97 00:06:08,380 --> 00:06:11,720 So we have seen before that slope is given a study done. 98 00:06:12,040 --> 00:06:13,870 Now you can find the slope like this. 99 00:06:13,870 --> 00:06:20,860 Also, if you have two points, you can find the slope as Y two minus Y, one by X2 minus X1. 100 00:06:21,250 --> 00:06:23,940 All right, let me take this over here. 101 00:06:24,190 --> 00:06:26,010 So we have learned the generic form. 102 00:06:26,320 --> 00:06:32,440 We have learned the form where we write X divided by the X intercept plus Y divided by the Y intercept 103 00:06:32,440 --> 00:06:33,190 is equal to one. 104 00:06:33,460 --> 00:06:37,840 And the next form that we learned about is Y is equal to imex policy. 105 00:06:38,180 --> 00:06:40,860 And this is the two point form that we discussed. 106 00:06:41,020 --> 00:06:48,190 And remember, we discussed that the slope of this line where two points are given is equal to Y to 107 00:06:48,190 --> 00:06:51,100 minus Y, one by X2, minus X one. 108 00:06:51,280 --> 00:06:56,470 So in this case, if the point is zero four and three zero, what would be the slope? 109 00:06:56,620 --> 00:06:59,320 It's zero minus four by three minus zero. 110 00:06:59,330 --> 00:06:59,610 Right. 111 00:06:59,800 --> 00:07:02,320 That is equal to minus four by three. 112 00:07:02,600 --> 00:07:04,290 Now you know the slope. 113 00:07:04,450 --> 00:07:07,990 Now can you write the equation of the line using this form? 114 00:07:08,140 --> 00:07:10,300 That is why is equal to and makes policy. 115 00:07:10,480 --> 00:07:11,530 Yes, we can do that. 116 00:07:11,530 --> 00:07:14,680 Right, because we know M is minus four by three. 117 00:07:14,930 --> 00:07:20,770 So the equation becomes why is equal to minus four by three X plus the Y intercept. 118 00:07:20,920 --> 00:07:22,970 Now what is the Y intercept over here. 119 00:07:23,320 --> 00:07:26,080 Over here you can see that this is the Y intercept, right. 120 00:07:26,200 --> 00:07:28,900 When X is equal to zero, Y is equal to four. 121 00:07:29,050 --> 00:07:30,700 So the Y intercept is four. 122 00:07:30,820 --> 00:07:36,460 So the equation of the line becomes Y is equal to minus four by three X plus four. 123 00:07:38,190 --> 00:07:43,370 All right, let's quickly summarize, we have learned four ways of writing the equation of a line. 124 00:07:43,650 --> 00:07:48,660 This is the generic form, then this is the form where we use X and Y intercepts. 125 00:07:48,990 --> 00:07:52,770 This is the form where we write Y is equal to mix policy. 126 00:07:52,950 --> 00:07:59,940 And we learned about the PowerPoint form where the equation of the line is given us Y minus Y one by 127 00:07:59,940 --> 00:08:05,610 X, minus X one is equal to Y two minus Y, one by X2 minus X one.