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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.