[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.72,0:00:03.06,Default,,0000,0000,0000,,- [Instructor] We're told\Na city bike rental service
Dialogue: 0,0:00:03.06,0:00:07.26,Default,,0000,0000,0000,,charges customers based on how\Nlong they rent the bicycle.
Dialogue: 0,0:00:07.26,0:00:11.16,Default,,0000,0000,0000,,The table shows the total\Ncost for renting a bicycle
Dialogue: 0,0:00:11.16,0:00:14.18,Default,,0000,0000,0000,,as a function of the\Nnumber of rental hours.
Dialogue: 0,0:00:14.18,0:00:15.46,Default,,0000,0000,0000,,So they say,
Dialogue: 0,0:00:15.46,0:00:19.71,Default,,0000,0000,0000,,"Complete the equation to\Nmodel the hourly rental cost."
Dialogue: 0,0:00:19.71,0:00:21.42,Default,,0000,0000,0000,,So what they really want us to do
Dialogue: 0,0:00:21.42,0:00:26.42,Default,,0000,0000,0000,,is have an equation of Y being,\Nwe could say a function of X
Dialogue: 0,0:00:28.07,0:00:31.14,Default,,0000,0000,0000,,that can describe what is going on here.
Dialogue: 0,0:00:31.14,0:00:33.45,Default,,0000,0000,0000,,So pause this video and have a go at it
Dialogue: 0,0:00:33.45,0:00:35.28,Default,,0000,0000,0000,,before we do this together.
Dialogue: 0,0:00:36.75,0:00:39.42,Default,,0000,0000,0000,,Alright, so let's just look\Nat the data a little bit
Dialogue: 0,0:00:39.42,0:00:42.12,Default,,0000,0000,0000,,and think about, okay, is\Nthis a linear relationship
Dialogue: 0,0:00:42.12,0:00:44.22,Default,,0000,0000,0000,,or is this something else?
Dialogue: 0,0:00:44.22,0:00:48.57,Default,,0000,0000,0000,,So when we increase our\Nrental hours by two,
Dialogue: 0,0:00:48.57,0:00:51.24,Default,,0000,0000,0000,,it looks like here, or when\Nwe go from one to three,
Dialogue: 0,0:00:51.24,0:00:55.41,Default,,0000,0000,0000,,we're increasing by two and\Nour cost is increasing by,
Dialogue: 0,0:00:55.41,0:00:59.46,Default,,0000,0000,0000,,let's see, to go from 12 to\N30, it's increasing by 18.
Dialogue: 0,0:00:59.46,0:01:01.83,Default,,0000,0000,0000,,See, when we go from\Nthree to five, once again,
Dialogue: 0,0:01:01.83,0:01:06.36,Default,,0000,0000,0000,,that's two more hours, and\Nit looks like every two hours
Dialogue: 0,0:01:06.36,0:01:11.36,Default,,0000,0000,0000,,we do indeed increase our cost\Nby 18, let me check again.
Dialogue: 0,0:01:11.76,0:01:16.76,Default,,0000,0000,0000,,Hours increase by 2 and\Ncost indeed increases by 18.
Dialogue: 0,0:01:17.43,0:01:21.99,Default,,0000,0000,0000,,So if we are increasing\Nby $18 every 2 hours,
Dialogue: 0,0:01:21.99,0:01:26.91,Default,,0000,0000,0000,,that's the same thing as\Nyou have a change in Y of $9
Dialogue: 0,0:01:28.95,0:01:32.47,Default,,0000,0000,0000,,every time you have a\Nchange in X of one hour.
Dialogue: 0,0:01:32.47,0:01:35.79,Default,,0000,0000,0000,,So it's $9 per hour.
Dialogue: 0,0:01:35.79,0:01:39.69,Default,,0000,0000,0000,,Now change in Y over change in\NX might look familiar to you.
Dialogue: 0,0:01:39.69,0:01:42.06,Default,,0000,0000,0000,,That is the slope of a line.
Dialogue: 0,0:01:42.06,0:01:44.04,Default,,0000,0000,0000,,So this is a linear relationship.
Dialogue: 0,0:01:44.04,0:01:48.90,Default,,0000,0000,0000,,It's going to have the form Y = MX + B,
Dialogue: 0,0:01:48.90,0:01:51.69,Default,,0000,0000,0000,,where this is the slope and\Nthis is the Y intercept.
Dialogue: 0,0:01:51.69,0:01:55.50,Default,,0000,0000,0000,,We just figured out the\Nslope, it is $9 per hour.
Dialogue: 0,0:01:55.50,0:02:00.50,Default,,0000,0000,0000,,So we could say Y = 9X plus\Nwhatever the Y intercept is.
Dialogue: 0,0:02:00.75,0:02:02.37,Default,,0000,0000,0000,,The Y intercept would be the minimum
Dialogue: 0,0:02:02.37,0:02:03.21,Default,,0000,0000,0000,,that they're going to charge you
Dialogue: 0,0:02:03.21,0:02:06.09,Default,,0000,0000,0000,,before they even bill you based on hours.
Dialogue: 0,0:02:06.09,0:02:07.20,Default,,0000,0000,0000,,And to figure out that,
Dialogue: 0,0:02:07.20,0:02:08.91,Default,,0000,0000,0000,,we just have to substitute\None of these points.
Dialogue: 0,0:02:08.91,0:02:11.70,Default,,0000,0000,0000,,We can say, okay, when X is 1, Y is 12.
Dialogue: 0,0:02:11.70,0:02:15.84,Default,,0000,0000,0000,,So let's just substitute\Nthat Y is 12 when X is 1.
Dialogue: 0,0:02:15.84,0:02:20.84,Default,,0000,0000,0000,,So 9 x 1 + B or 12 = 9 + B.
Dialogue: 0,0:02:22.05,0:02:23.19,Default,,0000,0000,0000,,You could do this in your head
Dialogue: 0,0:02:23.19,0:02:25.20,Default,,0000,0000,0000,,or you could subtract\Nnine from both sides,
Dialogue: 0,0:02:25.20,0:02:27.60,Default,,0000,0000,0000,,and you get 3 = B.
Dialogue: 0,0:02:27.60,0:02:30.57,Default,,0000,0000,0000,,So our equation, this\Nright over here is three.
Dialogue: 0,0:02:30.57,0:02:35.19,Default,,0000,0000,0000,,So we get Y = 9X + 3.
Dialogue: 0,0:02:35.19,0:02:38.16,Default,,0000,0000,0000,,One way to interpret this is even if you,
Dialogue: 0,0:02:38.16,0:02:41.19,Default,,0000,0000,0000,,just renting a bike before they\Neven charge you the hourly,
Dialogue: 0,0:02:41.19,0:02:43.47,Default,,0000,0000,0000,,they're gonna charge\Nyou $3 just to do that,
Dialogue: 0,0:02:43.47,0:02:46.65,Default,,0000,0000,0000,,and then they're going to charge\Nyou $9 per hour after that.
Dialogue: 0,0:02:46.65,0:02:47.70,Default,,0000,0000,0000,,And you can double check that.
Dialogue: 0,0:02:47.70,0:02:48.53,Default,,0000,0000,0000,,You could say,
Dialogue: 0,0:02:48.53,0:02:50.99,Default,,0000,0000,0000,,"Okay, well if I had to rent\Nthis bike for three hours,
Dialogue: 0,0:02:50.99,0:02:54.63,Default,,0000,0000,0000,,I'm gonna pay that $3 and then\NI'm gonna pay an extra $27
Dialogue: 0,0:02:54.63,0:02:57.39,Default,,0000,0000,0000,,for the hourly amount that I'm using it."
Dialogue: 0,0:02:57.39,0:02:59.70,Default,,0000,0000,0000,,27 + 3 is indeed $30.
Dialogue: 0,0:02:59.70,0:03:01.89,Default,,0000,0000,0000,,You could try out any of these other ones.