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We were able to already answer some interesting questions

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about the different plans at super yoga studio, using the equations we set up.

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But I'm a very visual guy.

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I wanna make sure I analyze the problem fully before I spend my hard earned dollars.

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What I wanna do now,

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is really see a visual representation for the relationsship between

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how many session I attend and how much its gonna cost me.

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I'm gonna do it for the trial plan and the basic plan.

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And to do that down here on the horizontal axis, I'm going to plot the number of sessions I attend.

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So S is equal to the number of session I attend.

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And here on the vertical axis,

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I'm gonna plot how much its gonna cost me depending on how how many session I attend.

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So C is equal is equal to my monthly cost.

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So let's think about these points right over here,

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and how these equations relates to what we might end up drawing.

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So the first point here, is that if I spend, if I go to no sessions,

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it's gonna cost me zero dollars.

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Where would I plot that?

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Right over here.

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If I attend no session, and I should have marked off zero here, its gonna cost me zero dollars.

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That is this point. Just like that.

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If I attend 1 session, it will be $12.

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Where would I plot that?

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Well, 1 session is gonna cost me $12.

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This is $15 so $12 is right around there.

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I'll put it there.

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If I attend 2 sessions, where would I plot that?

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Well, 2 session is going to cost me $24, so right about there.

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What about 3 sessions?

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I could keep going to 4, 5, 6 sessions,

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but I'll try 3, and I think you get the general idea.

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3 sessions cost $36.

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You see that all of these points seem to sit on a line.

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I will attempt my best to draw that line.

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And this line, it essentially describes all the possible combination of cost for a given number of sessions.

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So any point, specially if we allow fractional sessions.

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That is not conventional practice for most yoga studios but this one is a Super Yoga studio.

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and it allows you to attend 4 1/2 session or 1 1/2 sessions or exactly half a session.

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So if you attend half a session, its going to cost you $6.

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Another way to think about it is,

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if you attend zero session it'll be zero dollars.

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But then as you add a session, so you go one step right, it's going to cost you $12 more.

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so then you are gonna go up $12,

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so we went to right one, we went up $12. If we go to the right one more we go $12 up again.

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Because every session we add is gonna cost us $12 extra $12.

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We go from $0 to $12 to $24 to $36, if you add another session you add another $12.

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If you take away a session you will go $12 down.

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It is a kind of way of thinking about how steep this line is.

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Every time you go one to the right you go $12 up.

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Now, let's think about the same thing for the basic plan.

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How we might plot that.

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We will start with this point right over here.

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And basic plan, when I go to zero session it costs me $20.

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Where would I plot that on my graph?

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So zero session is going to cost me $20. That is that point over there.

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What about one session?

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Well one session is going to cost me $28.

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Another way of thinking about it: you pay $20 no matter what

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and as you add one session your total cost went up $8.

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This scale and this scale is not the same.

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If I did it to scale you would see these lines would look a lot steeper,

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and I would have to let this axis go a lot taller.

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But hopefully you get the idea, you add one session, we went up by $8.

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You add another session,

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so that was 1 and $28. That is that point over there.

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If you have 2 sessions, its gonna cost us $36.

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Where would we plot that?

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2 sessions are gonna cost $36 so, that is over there.

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Or another way to think of it.

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We were at $28 and we added a session, so we add another $8 to our cost.

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So $28 plus $8 gets us to $36.

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Now let's do this other point. And once again, we can keep going.

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Where would we plot the 3 sessions?

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So, if we attend 3 sessions, its gonna cost us $44.

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That's right about there.

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Once again we added a sessions and we added $8 to our cost.

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And you see these two seem to..., although I did not draw it as well as I can, these two seem to sit on a line.

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This by itself is interesting,

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but what might be even more interesting, is where these two lines intersect.

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We see that they have different steepnesses so at some point they should intersect

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And what's exciting about...

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Well, actually, I will let you think about it.

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What is exciting about where these two lines intersect?

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What does it tell us about the sessions and the cost at those points?

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I'll leave you there, and we will explore this more in the next video.