1 00:00:00,700 --> 00:00:07,330 High students so far, we have learned the general way in which we can express the equation of a straight 2 00:00:07,330 --> 00:00:07,700 line. 3 00:00:07,720 --> 00:00:13,750 Right now, let's see the next way in which we write the equation of a straight line that is X by three 4 00:00:13,930 --> 00:00:15,950 plus Y by four is equal to one. 5 00:00:16,190 --> 00:00:17,860 But how do you get from here to here? 6 00:00:18,250 --> 00:00:18,840 That's right. 7 00:00:18,850 --> 00:00:19,910 This equation over here. 8 00:00:20,140 --> 00:00:23,560 That's four X plus three Y is equal to twelve. 9 00:00:23,860 --> 00:00:26,260 Now, if you divide this throughout by 12. 10 00:00:26,260 --> 00:00:26,650 Right. 11 00:00:26,890 --> 00:00:28,730 You'll get to this equation over here. 12 00:00:28,780 --> 00:00:32,430 Let me show you how or here this becomes or X by 12. 13 00:00:32,590 --> 00:00:35,590 And I can write this as X divided by twelve. 14 00:00:35,590 --> 00:00:36,130 By four. 15 00:00:36,160 --> 00:00:36,500 Right. 16 00:00:36,790 --> 00:00:38,700 Plus this is three Y by 12. 17 00:00:38,920 --> 00:00:44,290 That can be written as Y divided by well by three and twelve by twelve is equal to one. 18 00:00:44,560 --> 00:00:49,780 So this twelve by four is your three over here and twelve by three is your four over here. 19 00:00:50,110 --> 00:00:56,770 Now the generic way of this form of writing the equation of a straight line is X divided by a plus Y 20 00:00:56,770 --> 00:00:59,170 divided by B is equal to one. 21 00:00:59,530 --> 00:01:01,810 All right, let me make some space over here. 22 00:01:02,140 --> 00:01:05,430 Now, there is some interesting things to note about this equation. 23 00:01:05,800 --> 00:01:12,470 This tree over here that you have is the X intercept, and this four is the Y intercept. 24 00:01:12,700 --> 00:01:13,810 What do I mean with that? 25 00:01:13,990 --> 00:01:16,450 Now, when X is equal to zero, right. 26 00:01:16,630 --> 00:01:18,750 Y is equal to four for this equation. 27 00:01:18,970 --> 00:01:21,250 That is what we call the Y intercept. 28 00:01:21,520 --> 00:01:23,070 That is X is equal to zero. 29 00:01:23,260 --> 00:01:25,000 You get Y is equal to four. 30 00:01:25,330 --> 00:01:30,010 Similarly, when Y is equal to zero, you get X is equal to three. 31 00:01:30,160 --> 00:01:32,500 And that is what we call the X intercept. 32 00:01:32,710 --> 00:01:37,480 Now let me mark these two points on our X Y plane over here. 33 00:01:37,830 --> 00:01:41,070 So that is three zero and this is zero for now. 34 00:01:41,120 --> 00:01:42,530 Let me join them together. 35 00:01:42,700 --> 00:01:47,290 Let's quickly discuss why this formula is true right now. 36 00:01:47,410 --> 00:01:48,750 Let's take any point. 37 00:01:48,760 --> 00:01:49,950 Be on this line. 38 00:01:50,200 --> 00:01:51,910 This is point B, X, Y. 39 00:01:52,350 --> 00:01:52,840 All right. 40 00:01:53,080 --> 00:01:57,350 Now, let me join B to the origin over here, OK? 41 00:01:58,210 --> 00:02:00,010 Now, let me mark these points. 42 00:02:00,020 --> 00:02:05,810 SPQR s OK, this is Q This is, this is this is ah. 43 00:02:06,220 --> 00:02:13,690 Now let's drop a perpendicular promise to y axis and the x axis. 44 00:02:13,690 --> 00:02:14,980 So that's about particular. 45 00:02:14,980 --> 00:02:16,250 And this is a perpendicular. 46 00:02:16,690 --> 00:02:17,160 All right. 47 00:02:17,410 --> 00:02:19,720 Now let this length over here be it. 48 00:02:20,140 --> 00:02:20,550 Right. 49 00:02:21,310 --> 00:02:22,330 And this is B right. 50 00:02:22,330 --> 00:02:24,550 Because over here we have E has the X intercept. 51 00:02:24,910 --> 00:02:28,900 That's E over here and over here we have B as the Y intercept. 52 00:02:29,080 --> 00:02:34,750 That is B over here already now and a nice triangle P Q are. 53 00:02:34,870 --> 00:02:36,340 So we have this triangle over here. 54 00:02:36,340 --> 00:02:36,670 Right. 55 00:02:36,950 --> 00:02:37,930 This is triangle P. 56 00:02:37,930 --> 00:02:38,470 Q are. 57 00:02:39,720 --> 00:02:46,380 You will see that the area of Triangle Peak you are is equal to offer in to be because the axes intersect 58 00:02:46,380 --> 00:02:47,310 at right angles. 59 00:02:49,160 --> 00:02:55,250 All right, now, another way of finding the area of this triangle peculiar would be finding the area 60 00:02:55,250 --> 00:02:58,400 of Triangle B askew, right. 61 00:02:59,180 --> 00:03:04,250 Triangle B, rescue plus area of triangle on. 62 00:03:06,780 --> 00:03:11,520 Right, so this this triangle over here is askew, this one over here. 63 00:03:11,780 --> 00:03:12,920 Yes, you are. 64 00:03:13,410 --> 00:03:13,910 All right. 65 00:03:14,790 --> 00:03:18,690 Now, what would be the area of Triangle B askew? 66 00:03:18,870 --> 00:03:22,400 That would be half being to this distance over here? 67 00:03:22,410 --> 00:03:22,710 Right. 68 00:03:22,840 --> 00:03:24,270 And what is this distance? 69 00:03:24,480 --> 00:03:27,120 This distance will be equal to X, right? 70 00:03:27,240 --> 00:03:32,450 Because this point over here is B, X, Y, but this distance is X right now. 71 00:03:32,460 --> 00:03:35,610 Therefore, this area will be half B into X. 72 00:03:35,790 --> 00:03:40,170 Similarly, this area will be half in the Y because this distance. 73 00:03:40,170 --> 00:03:40,500 Right. 74 00:03:40,650 --> 00:03:41,880 Is equal to it. 75 00:03:41,910 --> 00:03:43,350 Let me right that over here for you. 76 00:03:44,730 --> 00:03:52,080 This distance, right, is equal to X and this distance is equal to Y because we have taken B, X, 77 00:03:52,080 --> 00:03:52,380 Y. 78 00:03:52,680 --> 00:04:00,880 Now the area of Triangle BQE will be off being the X and the area of Triangle Square will be half in 79 00:04:00,910 --> 00:04:05,310 do Y, so that's equal to half B X plus half E white. 80 00:04:05,640 --> 00:04:06,200 All right. 81 00:04:06,220 --> 00:04:07,680 But make some space over here. 82 00:04:10,220 --> 00:04:19,010 Now, these two are equal, right, to let me cut out the half and I get a B is equal to B, X plus 83 00:04:19,220 --> 00:04:28,220 a Y now divided throughout with a B and you get X divided by eight is plus Y, baby is equal to one. 84 00:04:28,220 --> 00:04:32,180 And that is this equation which we discussed over here.