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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Yes, there are a lot of ways to come at this problem analytically but that will not always be the case. That is when we separate the heavyweights from the lightweights, when geogebra will shine.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Hi Bobby,

I used G (only) as my 'go to' prog for this and used its great abilities to quickly give a solution, but I also got some satisfaction in being able to find that alternative (I'd thought I wouldn't find one), which I did with trig and M and needed much more thinking time.

If you're there, I'm here, ready to continue from where we left off...but I'll need to go to bed soon-ish.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Okay, you want to know what we mean for the curve?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Yes please...I'm clueless. That was never covered in 4th-year high.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Did they cover graphing a line and such?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Not that I recall, but then I wasn't terribly attentive in class and my main aim was to drop out of school that year.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Without the jargon an equation is a thing where there are variables ( x, y, z, a... etc ) that are linked together by an equal sign.

x^2 + 5x + 2 = 0 is an equation. E=mc^2 is an equation, y = 16t^2 is an equation. x + y is not. Savvy?

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Savvy, kemo sabe.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Sometimes an equation has only one variable and we must try to solve for it and sometimes it has more than one.

x - 5 = 0 is an equation with one variable. y = 3x - 8 is an equation with 2 variables. If you follow up to here we need to sort of define one term here...

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Yes, I saw the multi-variable conic equations and didn't know what to do with them. I've used 'simultaneous equations' to eliminate variables...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

When we say solve an equation we mean find the value of the variables that make the equation true.

x + 3 = 9

If we say that x = 6 then

6 + 3 = 9 is true so 6 is a solution to that equation. 5 or anything else is not.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Understood...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Sometimes an equation can have more than one solution! For instance y = 3x + 9, x = 1 and y = 12 is a solution because 12 = 3 + 9. x = 2 and y = 15 is a solution because 15 = 3(2) + 9. Savvy?

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Yes, no probs with that.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Notice how each solution can be paired together to form what they call an ordered pair. How amazing.

We can get a lot of them (3,12), (6,15), (9,18)...

By the way they are called ordered pairs because they are a pair where the order counts, (6,12) is not the same as (12,6)

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

I think I may have heard that term, but I didn't know what it meant.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Now each one of those ordered pairs can be plotted on a piece of paper where y ( the second number) and x ( the first number ) are the vertical and horizontal axis. In geogebra enter ( 6 , 9 ).

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Done. I've done that before with, eg, A = ( 6, 9 ).

*Last edited by phrontister (2014-04-01 03:07:53)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Each ordered pair ( solution to the equation ) can be plotted just like that.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Yes...tried it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

If you draw a line through all 3 points then geogebra will give you a surprise.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

Hang on...I've lost track. What is the equation we're working on? Is it the one in post #63: y = 3x + 9?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

That is very good, I changed in the middle of this.

Let me get back on track, let's use the equation:

y = 3x + 9 and the 3 ordered pairs (1,12), (2,15), (3,18)

What do those 3 ordered pairs represent?

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,993

I'd anticipated that and entered the coordinates into G...which gave a straight line connecting the lot.

Oops. Sorry, but I didn't answer your Q. They're coordinates.

*Last edited by phrontister (2014-04-01 03:30:43)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,763

Look at the algebra pane and under Line, what is there?

**In mathematics, you don't understand things. You just get used to them.**

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