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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

**2. (0, -4) and (-4/3, 0)**

**3. (0, -5) (- 15/4, 0)**

**5. (2, 4) (2, 6)**

**6. (0, -2) (-2, 0)**

What do these look like once they're graphed? I've tried a bunch and keep getting it wrong. Help me!!

By the way, there should be 2 lines once graphed. Each 2 point sets are for one line.

I'm just here to get some help with an online math course I'm taking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

hi SlowlyFading,

Have a look at the diagram below.

I've 'colour-coded' them to make it easier to see which is which.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

Why are they all on one graph?

I'm just here to get some help with an online math course I'm taking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

Why are they all on one graph?

Strictly speaking, my diagram shows** four** graphs on a single set of axes.

And I did this to save time.

If you need four separate answers, just make 4 separate diagrams.

But sometimes, you need to put two or more lines onto a single set of axes, so you can see where they cross.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

There needs to be two lines on each graph, once graphed. *Each 2 point sets* are for one line. So for #2, (0, -4) is for one line and the other point set is for another line. That's one graph.

I'm just here to get some help with an online math course I'm taking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

I'm confused about what you want.

2. (0, -4) and (-4/3, 0)

That is two points so I showed them in red on my diagram with a line joining them.

3. (0, -5) (- 15/4, 0)

That's another two points, shown this time in blue, with a line joining them.

Perhaps you need to post the actual question wording that went with these coordinates.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

Okay, I'm going to try to explain it better.

My lesson is about liner equations, which states, "A system of linear equations is two or more linear equations that are solved at the same time. To solve a system of linear equations by graphing, we graph the equations on one coordinate plane. The solution is the point where the lines cross."

So, the line doesn't need to join them together. The graph needs two lines, not one line joining the coordinates. So, using the coordinates from #2; the graph needs to lines, one line from (0, -4) and another from (-4/3, 0). Not one line made from joining both coordinates.

Hopefully, this clarifies. By the way, I'm not sure if the lines will cross each other on every graph. It's okay if they're not..

Thanks!

I'm just here to get some help with an online math course I'm taking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,771

Hi SlowlyFading;

the graph needs to lines, one line from (0, -4) and another from (-4/3, 0)

Takes two points to determine a line. There are bajillions of lines that go through (0,-4).

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

hi SlowlyFading,

I understand the theory of systems of linear equations.

What I want is the exact wording of the questions you have been set.

It is not possible to draw a single line where only one point is given.

When you know two points, you can join them with a line.

Then if you have another two points, you can join them with another line.

Then you can look to see where the lines cross.

I have decided to assume that Q2 and Q3 are meant to be taken as such a system.

The diagram below then shows what answer you would get.

If that is not what the questions ask, you will have to give the exact wording of the questions.

Bob

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

It says, "Graph the following using the given points using the system of linear equations."

The ones I can't get are:

2. (0, -4) and (-4/3, 0)

3. (0, -5) and (- 15/4, 0)

5. (2, 4) and (2, 6)

6. (0, -2) and (-2, 0)

And under each problem would be a graph where I draw my lines.

I'm just here to get some help with an online math course I'm taking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

Well one point is not enough to fix a line. (see latest diagram)

So what I did in post 2 is the best I can offer for this. Sorry.

Bob

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Hi SlowlyFading!

The quote says "Graph the following using the given points using the system of linear equations."

This instruction is poorly worded. I've taught algebra for over 40 years but I can't understand what

this is asking. Perhaps if it comes from a book and the book has had several examples using this

terminology one could figure out what is being asked.

As mentioned in the previous posts it take TWO points to determine a straight line. Then it takes

TWO such lines to determine a system of equations and a point of crossing (if they cross. Distinct

parallel lines do not cross.)

I would think that since the question says "using the system of linear equations" that one would have

to first get the equations for the two lines (like #2 and #3 together). Then one could solve for the

exact point where they cross. Often it is difficult to get better than just an approximation to the

point where they cross since the point may involve fractions or decimals: difficult to figure out from

a drawn graph. If using a graphing calculator then one can zoom in to get better approximations.

Also one doesn't need the system of equations to just graph the lines. The system is needed to

get an accurate point of intersection.

May you be much blessed in your mathematical endeavors!

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

Oh, shame on me. You guys were right (of course).

Okay, I found the other points, "the given points" are points I have to find. I made an error in thinking I already had them all it it was confusing me greatly.

HOPEFULLY! This works better. Sorry about my screw up guys..

2. (0, -4) (-4/3, 0) and (1, -1) (2, -2)

3. (0, -5)(- 15/4, 0) and

y = x + 2

m = 1

b = 2

5. (2, 4) (3, 6) and (2, 1) (I can't find the other point for some reason, grr..) The equation the point needs to be found from is x + y = 3.

6. I found m = 1/3 b =-1 from x = 3 - 3y

and

(0, -2) and (-2, 0)

Sorry for my mistakes. I hope this works better! Thanks for all the help!

I'm just here to get some help with an online math course I'm taking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

Arrrhhh! At last the question makes sense.

Q2 shown in red.

Q3 shown in blue

Q5. shown in green.

You have asked about x + y = 3 before because I remember making a diagram for this.

You just need the x and y numbers to add up to a total of 3. eg. (3,0) (2,1) (1,2) (0,3)

Q6 shown in purple.

I plotted the b point (0,-1) and then used the gradient ... 3 across 1 up, to make more points.

Bob

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Hi Bob!

Nice graphs! What program are you using to get those?

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,126

hi noelevans,

It's called Geometer's Sketchpad.

It's not free like Geogebra, but has some excellent features.

Bob

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**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

That's exactly what I needed! Thanks a million.

I'm just here to get some help with an online math course I'm taking.

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Thanks, Bob

I'll check into it and probably some free ones too.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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