0:00:00.720,0:00:03.060
- [Instructor] We're told[br]a city bike rental service

0:00:03.060,0:00:07.260
charges customers based on how[br]long they rent the bicycle.

0:00:07.260,0:00:11.160
The table shows the total[br]cost for renting a bicycle

0:00:11.160,0:00:14.175
as a function of the[br]number of rental hours.

0:00:14.175,0:00:15.457
So they say,

0:00:15.457,0:00:19.710
"Complete the equation to[br]model the hourly rental cost."

0:00:19.710,0:00:21.420
So what they really want us to do

0:00:21.420,0:00:26.420
is have an equation of Y being,[br]we could say a function of X

0:00:28.068,0:00:31.140
that can describe what is going on here.

0:00:31.140,0:00:33.450
So pause this video and have a go at it

0:00:33.450,0:00:35.283
before we do this together.

0:00:36.750,0:00:39.420
Alright, so let's just look[br]at the data a little bit

0:00:39.420,0:00:42.120
and think about, okay, is[br]this a linear relationship

0:00:42.120,0:00:44.220
or is this something else?

0:00:44.220,0:00:48.570
So when we increase our[br]rental hours by two,

0:00:48.570,0:00:51.240
it looks like here, or when[br]we go from one to three,

0:00:51.240,0:00:55.410
we're increasing by two and[br]our cost is increasing by,

0:00:55.410,0:00:59.460
let's see, to go from 12 to[br]30, it's increasing by 18.

0:00:59.460,0:01:01.830
See, when we go from[br]three to five, once again,

0:01:01.830,0:01:06.360
that's two more hours, and[br]it looks like every two hours

0:01:06.360,0:01:11.360
we do indeed increase our cost[br]by 18, let me check again.

0:01:11.763,0:01:16.763
Hours increase by 2 and[br]cost indeed increases by 18.

0:01:17.430,0:01:21.990
So if we are increasing[br]by $18 every 2 hours,

0:01:21.990,0:01:26.910
that's the same thing as[br]you have a change in Y of $9

0:01:28.950,0:01:32.468
every time you have a[br]change in X of one hour.

0:01:32.468,0:01:35.790
So it's $9 per hour.

0:01:35.790,0:01:39.690
Now change in Y over change in[br]X might look familiar to you.

0:01:39.690,0:01:42.060
That is the slope of a line.

0:01:42.060,0:01:44.040
So this is a linear relationship.

0:01:44.040,0:01:48.900
It's going to have the form Y = MX + B,

0:01:48.900,0:01:51.690
where this is the slope and[br]this is the Y intercept.

0:01:51.690,0:01:55.500
We just figured out the[br]slope, it is $9 per hour.

0:01:55.500,0:02:00.500
So we could say Y = 9X plus[br]whatever the Y intercept is.

0:02:00.750,0:02:02.370
The Y intercept would be the minimum

0:02:02.370,0:02:03.210
that they're going to charge you

0:02:03.210,0:02:06.090
before they even bill you based on hours.

0:02:06.090,0:02:07.200
And to figure out that,

0:02:07.200,0:02:08.910
we just have to substitute[br]one of these points.

0:02:08.910,0:02:11.700
We can say, okay, when X is 1, Y is 12.

0:02:11.700,0:02:15.840
So let's just substitute[br]that Y is 12 when X is 1.

0:02:15.840,0:02:20.840
So 9 x 1 + B or 12 = 9 + B.

0:02:22.050,0:02:23.190
You could do this in your head

0:02:23.190,0:02:25.200
or you could subtract[br]nine from both sides,

0:02:25.200,0:02:27.600
and you get 3 = B.

0:02:27.600,0:02:30.570
So our equation, this[br]right over here is three.

0:02:30.570,0:02:35.190
So we get Y = 9X + 3.

0:02:35.190,0:02:38.160
One way to interpret this is even if you,

0:02:38.160,0:02:41.190
just renting a bike before they[br]even charge you the hourly,

0:02:41.190,0:02:43.470
they're gonna charge[br]you $3 just to do that,

0:02:43.470,0:02:46.650
and then they're going to charge[br]you $9 per hour after that.

0:02:46.650,0:02:47.700
And you can double check that.

0:02:47.700,0:02:48.533
You could say,

0:02:48.533,0:02:50.986
"Okay, well if I had to rent[br]this bike for three hours,

0:02:50.986,0:02:54.630
I'm gonna pay that $3 and then[br]I'm gonna pay an extra $27

0:02:54.630,0:02:57.390
for the hourly amount that I'm using it."

0:02:57.390,0:02:59.700
27 + 3 is indeed $30.

0:02:59.700,0:03:01.893
You could try out any of these other ones.