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# Super Yoga plans: Plotting points

Video transcript

We were able to already answer
some interesting questions about the different plans
at the Super Yoga Studio, using the equations we set up. But I'm a very visual
guy, and I want to make sure that I
analyze the problem fully before I spend my
hard earned dollars. And what I want to
do now is really see a visual representation for
the relationship between how many sessions I attend, and
how much it's going to cost me. And I'm going to do it for the
trial plan and the basic plan. And to do that, down here
on the horizontal axis, I'm going to plot the number
of sessions that I attend. So s, that is equal to
the number of sessions I attend per month. And then here on
the vertical axis I'm going to plot how much
it's going to cost me, depending on how many
sessions I attend. So c is equal to
my monthly cost. So let's think about these
points right over here. And then even also think about
how this equation relates to what we might end up drawing. So the first point here is
that if I go to no sessions, it's going to cost me $0.00. So where would I plot
that right over here? Well, if I attend no sessions,
and I should have marked off a 0 right over here, it's
going to cost me $0.00. So it's this point,
just like that. Now let's think about
if I attend one session. If I attend one session,
it'll be $12.00. Where would I plot that? Well, one session is
going to cost me $12.00, see this is $15.00, so $12.00 is
going to be right around there. So I'll put it right over there. And if I attend two sessions,
where would I plot that? Well, two sessions are
going to cost me $24.00, so we get the right about there. And then what about
three sessions? And I could keep going four,
five, six, on, and on, and on. But let's just
try three, I think you'll get the general idea. Three sessions cost $36.00. And you see that all of these
points seem to sit on a line. And I can attempt, I'll attempt
my best, to draw that line. And this line
essentially describes all of the possible
combinations of cost for a given number of sessions. So any point here,
especially if we're assuming that we allow
fractional sessions. That's not conventional
practice for most yoga studios, but this one is a
super yoga studio, so it allows you to attend four
and one half sessions, or one and one half sessions, or
exactly half a session. So if you attend half a session
it's going to cost you $6.00 Another way to think about it
is if you attend zero sessions it'll be $0.00, but then
as you add a session, so you go to the right one step,
it's going to cost you $12.00 more. So then you're going
to go up $12.00. So we went to the right
one, we went up 12. If we go to the right one again,
we're going to go up 12 again. Because every session
we add is going to cost us 12 extra dollars. We go from 0 to 12 to 24. If you add another session
you go up 12 again. If you take away a
session, you'll go down 12. And so it's a kind
of a way of thinking about how steep this line is. Every time you go one to the
right, you're going 12 up. Now let's think about the
same thing for the basic plan, how we might actually plot that. So I'll start with this
point right over here. And the basic plan, when I go
to zero sessions it costs me $20.00. Where would I plot
that on my graph? So zero sessions are
going to cost me $20.00. That's that point
right over there. What about one session. Well, one session is
going to cost me $28.00. And another way to think about
it, you pay 20 no matter what, and as you add one session,
your total cost went up by 8. This scale and this
scale is not the same. If I did it to
scale, then you would see these lines would
look a lot steeper, and I would have to make this
axis go a lot, lot taller. But hopefully you get the idea. You add one session,
we went up by 8. You add another
session, so that was 128, that's that point
right over there. So if you have two sessions,
it's going to cost us $36.00. Where would we plot that? Two sessions are
going to cost $36.00. So that is right over there. Or another way to think of it. We were at 28, we
added another session, so we're going to
add $8 to our cost. So 28 plus 8 gets us to $36.00 Now let's do this other point
once again, we can keep going. Where would we plot
the three sessions. So if we attend three sessions,
it's going to cost us $44.00. So that's right about there. Once again, we added the session
and we added $8.00 to our cost. And you see these two
seem to sit on a line. Although I didn't draw
it as well as I can, so these two seem
to sit on a line. Now this by itself
is interesting. But what might be
even more interesting is where these two
lines intersect. We see that they have different
steepnesses, so at some point they should intersect. And what's exciting
about, well, actually I'll let you think about it. What is exciting about where
these two lines intersect? What does it tell us
about the sessions, and the cost at those points? And I'll leave you
there, and we'll explore this more
in the next video.