WEBVTT 00:00:00.720 --> 00:00:03.060 - [Instructor] We're told a city bike rental service 00:00:03.060 --> 00:00:07.260 charges customers based on how long they rent the bicycle. 00:00:07.260 --> 00:00:11.160 The table shows the total cost for renting a bicycle 00:00:11.160 --> 00:00:14.175 as a function of the number of rental hours. 00:00:14.175 --> 00:00:15.457 So they say, 00:00:15.457 --> 00:00:19.710 "Complete the equation to model the hourly rental cost." 00:00:19.710 --> 00:00:21.420 So what they really want us to do 00:00:21.420 --> 00:00:26.420 is have an equation of Y being, we could say a function of X 00:00:28.068 --> 00:00:31.140 that can describe what is going on here. 00:00:31.140 --> 00:00:33.450 So pause this video and have a go at it 00:00:33.450 --> 00:00:35.283 before we do this together. 00:00:36.750 --> 00:00:39.420 Alright, so let's just look at the data a little bit 00:00:39.420 --> 00:00:42.120 and think about, okay, is this a linear relationship 00:00:42.120 --> 00:00:44.220 or is this something else? 00:00:44.220 --> 00:00:48.570 So when we increase our rental hours by two, 00:00:48.570 --> 00:00:51.240 it looks like here, or when we go from one to three, 00:00:51.240 --> 00:00:55.410 we're increasing by two and our cost is increasing by, 00:00:55.410 --> 00:00:59.460 let's see, to go from 12 to 30, it's increasing by 18. 00:00:59.460 --> 00:01:01.830 See, when we go from three to five, once again, 00:01:01.830 --> 00:01:06.360 that's two more hours, and it looks like every two hours 00:01:06.360 --> 00:01:11.360 we do indeed increase our cost by 18, let me check again. 00:01:11.763 --> 00:01:16.763 Hours increase by 2 and cost indeed increases by 18. 00:01:17.430 --> 00:01:21.990 So if we are increasing by $18 every 2 hours, 00:01:21.990 --> 00:01:26.910 that's the same thing as you have a change in Y of $9 00:01:28.950 --> 00:01:32.468 every time you have a change in X of one hour. 00:01:32.468 --> 00:01:35.790 So it's $9 per hour. 00:01:35.790 --> 00:01:39.690 Now change in Y over change in X might look familiar to you. 00:01:39.690 --> 00:01:42.060 That is the slope of a line. 00:01:42.060 --> 00:01:44.040 So this is a linear relationship. 00:01:44.040 --> 00:01:48.900 It's going to have the form Y = MX + B, 00:01:48.900 --> 00:01:51.690 where this is the slope and this is the Y intercept. 00:01:51.690 --> 00:01:55.500 We just figured out the slope, it is $9 per hour. 00:01:55.500 --> 00:02:00.500 So we could say Y = 9X plus whatever the Y intercept is. 00:02:00.750 --> 00:02:02.370 The Y intercept would be the minimum 00:02:02.370 --> 00:02:03.210 that they're going to charge you 00:02:03.210 --> 00:02:06.090 before they even bill you based on hours. 00:02:06.090 --> 00:02:07.200 And to figure out that, 00:02:07.200 --> 00:02:08.910 we just have to substitute one of these points. 00:02:08.910 --> 00:02:11.700 We can say, okay, when X is 1, Y is 12. 00:02:11.700 --> 00:02:15.840 So let's just substitute that Y is 12 when X is 1. 00:02:15.840 --> 00:02:20.840 So 9 x 1 + B or 12 = 9 + B. 00:02:22.050 --> 00:02:23.190 You could do this in your head 00:02:23.190 --> 00:02:25.200 or you could subtract nine from both sides, 00:02:25.200 --> 00:02:27.600 and you get 3 = B. 00:02:27.600 --> 00:02:30.570 So our equation, this right over here is three. 00:02:30.570 --> 00:02:35.190 So we get Y = 9X + 3. 00:02:35.190 --> 00:02:38.160 One way to interpret this is even if you, 00:02:38.160 --> 00:02:41.190 just renting a bike before they even charge you the hourly, 00:02:41.190 --> 00:02:43.470 they're gonna charge you $3 just to do that, 00:02:43.470 --> 00:02:46.650 and then they're going to charge you $9 per hour after that. 00:02:46.650 --> 00:02:47.700 And you can double check that. 00:02:47.700 --> 00:02:48.533 You could say, 00:02:48.533 --> 00:02:50.986 "Okay, well if I had to rent this bike for three hours, 00:02:50.986 --> 00:02:54.630 I'm gonna pay that $3 and then I'm gonna pay an extra $27 00:02:54.630 --> 00:02:57.390 for the hourly amount that I'm using it." 00:02:57.390 --> 00:02:59.700 27 + 3 is indeed $30. 00:02:59.700 --> 00:03:01.893 You could try out any of these other ones.