- [Instructor] We're told a city bike rental service
charges customers based on how long they rent the bicycle.
The table shows the total cost for renting a bicycle
as a function of the number of rental hours.
So they say,
"Complete the equation to model the hourly rental cost."
So what they really want us to do
is have an equation of Y being, we could say a function of X
that can describe what is going on here.
So pause this video and have a go at it
before we do this together.
Alright, so let's just look at the data a little bit
and think about, okay, is this a linear relationship
or is this something else?
So when we increase our rental hours by two,
it looks like here, or when we go from one to three,
we're increasing by two and our cost is increasing by,
let's see, to go from 12 to 30, it's increasing by 18.
See, when we go from three to five, once again,
that's two more hours, and it looks like every two hours
we do indeed increase our cost by 18, let me check again.
Hours increase by 2 and cost indeed increases by 18.
So if we are increasing by $18 every 2 hours,
that's the same thing as you have a change in Y of $9
every time you have a change in X of one hour.
So it's $9 per hour.
Now change in Y over change in X might look familiar to you.
That is the slope of a line.
So this is a linear relationship.
It's going to have the form Y = MX + B,
where this is the slope and this is the Y intercept.
We just figured out the slope, it is $9 per hour.
So we could say Y = 9X plus whatever the Y intercept is.
The Y intercept would be the minimum
that they're going to charge you
before they even bill you based on hours.
And to figure out that,
we just have to substitute one of these points.
We can say, okay, when X is 1, Y is 12.
So let's just substitute that Y is 12 when X is 1.
So 9 x 1 + B or 12 = 9 + B.
You could do this in your head
or you could subtract nine from both sides,
and you get 3 = B.
So our equation, this right over here is three.
So we get Y = 9X + 3.
One way to interpret this is even if you,
just renting a bike before they even charge you the hourly,
they're gonna charge you $3 just to do that,
and then they're going to charge you $9 per hour after that.
And you can double check that.
You could say,
"Okay, well if I had to rent this bike for three hours,
I'm gonna pay that $3 and then I'm gonna pay an extra $27
for the hourly amount that I'm using it."
27 + 3 is indeed $30.
You could try out any of these other ones.