1 00:00:00,000 --> 00:00:00,790 2 00:00:00,790 --> 00:00:03,629 On Monday morning, there were 12 inches 3 00:00:03,629 --> 00:00:05,290 of snow on the ground. 4 00:00:05,290 --> 00:00:08,129 The weather warmed up, and by Tuesday morning, 5 00:00:08,130 --> 00:00:09,520 2 inches had melted. 6 00:00:09,519 --> 00:00:11,439 All right, so we'll have 10 left. 7 00:00:11,439 --> 00:00:14,349 2 more inches melted by Wednesday morning. 8 00:00:14,349 --> 00:00:16,980 This pattern continued throughout the week until no 9 00:00:16,980 --> 00:00:18,300 more snow was left. 10 00:00:18,300 --> 00:00:21,280 So they're essentially saying that we had 12 inches of snow 11 00:00:21,280 --> 00:00:24,789 on the ground on Monday and that every day after that, two 12 00:00:24,789 --> 00:00:25,640 inches melted. 13 00:00:25,640 --> 00:00:28,219 So after Tuesday, you'd have 10 inches, and after 14 00:00:28,219 --> 00:00:29,779 Wednesday, you'd have eight inches, and 15 00:00:29,780 --> 00:00:31,220 that pattern continued. 16 00:00:31,219 --> 00:00:34,640 And what they say is create an equation and a graph to show 17 00:00:34,640 --> 00:00:37,789 the relationship between the day and the amount of snow on 18 00:00:37,789 --> 00:00:38,329 the ground. 19 00:00:38,329 --> 00:00:41,670 So let's define a variable that tells us how far away we 20 00:00:41,670 --> 00:00:42,670 are from Monday. 21 00:00:42,670 --> 00:00:49,010 So let's let x equal days after Monday. 22 00:00:49,009 --> 00:00:57,039 23 00:00:57,039 --> 00:01:03,049 And then let y be equal to inches of snow on the ground. 24 00:01:03,049 --> 00:01:11,560 25 00:01:11,560 --> 00:01:17,109 So, one way to think about it is, OK, when x is 0, when 26 00:01:17,109 --> 00:01:19,905 we're on Monday, when we're 0 days after Monday, we're going 27 00:01:19,905 --> 00:01:23,879 to have 12 inches of snow on the ground, and every day 28 00:01:23,879 --> 00:01:27,280 after that, we're going to lose two inches. 29 00:01:27,280 --> 00:01:30,549 So if we're on Tuesday, we're going to have 2 inches times 30 00:01:30,549 --> 00:01:33,974 1, because Tuesday is one day, so if x is 1, that means we're 31 00:01:33,974 --> 00:01:34,890 on Tuesday. 32 00:01:34,890 --> 00:01:40,129 If x is 2, that means we're 2 times 2, we've lost 4 inches, 33 00:01:40,129 --> 00:01:42,769 which is what the case is on Wednesday. 34 00:01:42,769 --> 00:01:47,280 So this is our equation for the relationship between the 35 00:01:47,280 --> 00:01:49,370 day and the amount of snow on the ground. 36 00:01:49,370 --> 00:01:54,885 x is the day, how many days after Monday, and then y is 37 00:01:54,885 --> 00:01:57,440 the inches of the snow left on the ground. 38 00:01:57,439 --> 00:01:59,670 We start with 12, and then every day we 39 00:01:59,670 --> 00:02:02,060 lose exactly two inches. 40 00:02:02,060 --> 00:02:03,310 Now let's graph this. 41 00:02:03,310 --> 00:02:06,040 42 00:02:06,040 --> 00:02:11,009 So I'll make my vertical axis the y-axis, that's inches on 43 00:02:11,008 --> 00:02:11,779 the ground. 44 00:02:11,780 --> 00:02:17,419 y is equal to inches left on the ground. 45 00:02:17,419 --> 00:02:22,399 And then the horizontal axis, that is our x-axis-- let me 46 00:02:22,400 --> 00:02:31,939 scroll down a little bit-- this is days after Monday. 47 00:02:31,939 --> 00:02:35,199 48 00:02:35,199 --> 00:02:40,789 And so we have 0 days after Monday, we have 1, 2, 49 00:02:40,789 --> 00:02:46,000 3, 4, 5, and 6. 50 00:02:46,000 --> 00:02:51,629 And then on Monday, which is exactly 0 days after Monday, 51 00:02:51,629 --> 00:02:54,379 that is Monday, we have 12 inches on the ground. 52 00:02:54,379 --> 00:02:59,969 So I'll do it up here, so we have 12 inches on the ground 53 00:02:59,969 --> 00:03:00,210 right there. 54 00:03:00,210 --> 00:03:02,740 And actually, I could do a table if you like. 55 00:03:02,740 --> 00:03:04,420 Let me draw this. 56 00:03:04,419 --> 00:03:11,609 So if we do x and y, this is the days after Monday, so 57 00:03:11,610 --> 00:03:16,050 there's 0, 1, 2, 3, 4, 5, 6. 58 00:03:16,050 --> 00:03:19,730 And then on the first day, we have 12 inches, on Monday, 0 59 00:03:19,729 --> 00:03:20,769 days after Monday. 60 00:03:20,770 --> 00:03:22,610 Then we lose two inches each day. 61 00:03:22,610 --> 00:03:28,600 On day 1 we have 10, day 2, 8, 6, 4, 2, 0. 62 00:03:28,599 --> 00:03:29,689 So let's plot these points. 63 00:03:29,689 --> 00:03:33,240 We already plotted 0, 12 in that blue color. 64 00:03:33,240 --> 00:03:35,820 Now let's plot 1, 10. 65 00:03:35,819 --> 00:03:38,504 1, 10 is right about there. 66 00:03:38,504 --> 00:03:41,689 It'll be right over there. 67 00:03:41,689 --> 00:03:45,500 Then we can plot 2, 8. 68 00:03:45,500 --> 00:03:47,729 So 2 days after Monday, we have 8 69 00:03:47,729 --> 00:03:50,449 inches left on the ground. 70 00:03:50,449 --> 00:03:53,579 So this is on Wednesday, so that's 8 inches. 71 00:03:53,580 --> 00:04:00,650 And then on 3 days after Monday, we have 6 inches on 72 00:04:00,650 --> 00:04:01,900 the ground. 73 00:04:01,900 --> 00:04:05,950 74 00:04:05,949 --> 00:04:08,339 You can see that a line is forming here. 75 00:04:08,340 --> 00:04:12,810 And then if we go to 4 days after Monday, we have 4 inches 76 00:04:12,810 --> 00:04:14,060 on the ground. 77 00:04:14,060 --> 00:04:16,809 78 00:04:16,809 --> 00:04:18,890 So that is 4. 79 00:04:18,889 --> 00:04:22,849 And then 5 days after Monday, we have 2 80 00:04:22,850 --> 00:04:24,100 inches on the ground. 81 00:04:24,100 --> 00:04:27,340 82 00:04:27,339 --> 00:04:31,349 And then finally, on the sixth day, 6 days after Monday-- so 83 00:04:31,350 --> 00:04:34,650 what are we at, Sunday now-- we are going to have no inches 84 00:04:34,649 --> 00:04:36,549 on the ground. 85 00:04:36,550 --> 00:04:38,449 So that's that right there. 86 00:04:38,449 --> 00:04:41,579 And you can see that there's this line that formed, because 87 00:04:41,579 --> 00:04:43,719 this is a linear relationship. 88 00:04:43,720 --> 00:04:45,230 It looks a little curvy because I didn't draw it 89 00:04:45,230 --> 00:04:47,689 perfectly, but that is a line. 90 00:04:47,689 --> 00:04:48,660 So we've done everything. 91 00:04:48,660 --> 00:04:50,010 We've created the equation. 92 00:04:50,009 --> 00:04:52,029 We start with 12 inches, every day after 93 00:04:52,029 --> 00:04:53,500 that we lose two inches. 94 00:04:53,500 --> 00:04:57,050 And we showed a graph that depicts the relationship. 95 00:04:57,050 --> 00:04:57,400