hi SlowlyFading,

Have a look at the diagram below. 

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

Bob

Uploaded Images

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

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

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).

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.

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!

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

Uploaded Images

hi noelevans,

It's called Geometer's Sketchpad.

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

Bob

Thanks, Bob

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