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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

a: 3x - y = -9

...which is the same as y=3x+9.

"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: 105,688

That is correct.

What do those 3 coordinates really represent?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

Ordered pair solutions to the equation, verified by the straight connecting line.

"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: 105,688

Clear the drawing area and in the input bar enter y = 3x + 9.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

It created a slider for x, and under 'Number' has X=1 and Y=12

*Last edited by phrontister (2014-04-01 04:00:39)*

"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: 105,688

y = 3x + 9, sorry I was in caps lock.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

That gave a sloping straight line. Are the coordinates of any point along that line an ordered pair solution to the equation?

*Last edited by phrontister (2014-04-01 04:06:17)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,688

Yep! Use the point on object tool and place a point on that line. Now move the arrow keys and read from the algebra pane the coordinates of the point. Each first number in the parentheses is an x and the second number is the y. Plug them into the equation and you will get a balanced equation. The right hand side lovingly called the RHS and the other side LHS. They will be equal algebraically, meaning they are solutions to the equation.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

Yes, that works...but I can't use the arrow keys to move the point to integer solutions.

*Last edited by phrontister (2014-04-01 04:13:19)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,688

There is a way to do that using a slider. Are you able to move the point though?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

Yes...because I placed it away from the x and y axes, otherwise the point moves along the axis on which it is placed.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,688

That is because it became attached to the x or y axis instead of the equation we are interested in.

So, very loosely we can the say that the graph of an equation is the set of points that balance or solve the equation.

All clear to this point ( no pun intended ).

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

Yes, I understand all of this so far...but I also understand what my eyelids are telling me, which is that they need to be in bed! I'll have to leave it here, to be continued...

Thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,688

I knew you already knew but now we have established a common terminology and will get to circles and integrals next. Have a good night.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,435

Hi Bobby,

Ready to learn now about circles and integrals, but the going may be slow because this is all new territory for me...

Because of our time difference and my work commitments I may not be able to spend much concentrated time at it, though.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,688

Hi;

I am sorry, where did we leave off?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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