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Graphing


From: Anonymous
Date: Fri, 18 Aug 1995 13:40:01 -0700
Subject: lots of algebra

I've got more questions, this time concerning graphing. I've pretty much
forgotten everything, but I know how to plot points.

How do I solve this? 

        Give 4 ordered pairs which are solutions to the equation 3x + y = 1.
I have the answers, but I want to know how to do it. Help me out. 

        For each equation in exercises 11-14 pick 4 values for x and
evaluate y depending on the selected values of X. I picked (3,3)  (1,1)
(-1,-1)  (-3,-3) then you plot the points and connect them. This leads into
problem 11. 

y = 2x - 4. What are you supposed to do? another one is y=-3x+1. There is a
whole page of this stuff. Help is appreciated quickly.

     15. For the equation 2x-3y=6, first solve for y in terms of x then
graph the line using the procedure described for problems 11-14. (2 of them
are above)

Other stuff. Solve each of the following systems of equations by linear
combination. Check the solution by placing the ordered pair in both equations. 

3x+y=9                                  x+y=17
2x-y=6                                  8x-5y=-20

Also how do I graph the line 2x-3y=6
What is the slope of the line connecting the points (2,3) and (-2,4)
What is the slope of the line 3x-5y=8                   (What do I do on this?)
name 3 pts. which are on the graph of the line 3x+4y=12.

Thanks in advance. I use to know all this stuff, but last year I did
geometry and forgot most of this stuff. Please don't give me the anwsers,
but show me what to do and why your doing it. Thanks.


Date: 808781193
From: Doctor Ken
Subject: Re: lots of algebra

Hello!

>How do I solve this? 
>        Give 4 ordered pairs which are solutions to the equation 3x + y = 1.
>I have the answers, but I want to know how to do it. Help me out. 

Well, you can pretty much just pick a value for x at random, then plug it
in to the equation and see what x has to be.  For instance, using the
random number 17  (pretty random, huh?), we get 3*17 + y = 1, i.e.
51 + y = 1.  It seems clear that y must be -50.  So the ordered pair 
(17, -50) is a solution to the equation.  

Let's try another one.  Pick x to be 3.  Then what is y?  Do this a couple 
more times, and you'll have done the problem.

>        For each equation in exercises 11-14 pick 4 values for x and
>evaluate y depending on the selected values of X I picked (3,3)  (1,1)
>(-1,-1)  (-3,-3) then you plot the points and connect them. 

What was the equation you were working with here?  I hope it was y = x.
The basic idea here is the same as the first problem: pick an x value
at random, then plug it in for x and figure out what y is. Then you can
plot the points, and connect the dots like it says.

>this leads into problem 11. 
>y = 2x - 4. What are you supposed to do? 

I assume they mean to do the same thing, pick a value for x and plug it in
to the equation, then figure out what y is.  Then take the ordered pair (x,y)
and plot it.  Do that for 3 more different values of x, and then connect the
dots.

>Another one is y=-3x+1. There is a whole page of this stuff. Help is
>appreciated quickly.
>
>     15. For the equation 2x-3y=6, first solve for y in terms of x then
>graph the line using the procedure described for problems 11-14. (2 of them
>are above)

When they say "solve for y", they mean manipulate the equation until all that
you have on one side of the equation is y, and the other side has no y's in 
it at all.  For example, if they had given you the equation 5x + 8y = 3, 
I think the first thing I'd do is move the 5x over to the other side of the
equation, to get 8y = 3 - 5x.  Then we want to get rid of the y, right?  To
do that, we can just divide both sides of the equation by 8, to get this:
y = 3/8 - 5y/8.  Does that make sense?  

From here, you'd use the same method you used before to draw the graph of
this function.

>Other stuff. Solve each of the following systems of equations by linear
>combination. Check the solution by placing the ordered pair in both equations. 
>
>3x+y=9                                  x+y=17
>2x-y=6                                  8x-5y=-20

Here, I'll give you a similar example.  Look at the system
2x + 3y = 7
 x - 2y = 8

The method I like the best is to solve one of the equations for one of the 
variables, and then make a substitution into the other equation.  So we could
solve the first equation for x:
2x = 7 - 3y
 x = 7/2 - 3y/2
and then plug this value for x into the other equation:
     x       - 2y = 8    substitute
(7/2 - 3y/2) - 2y = 8    multiply by 2
   7 - 3y  -   4y = 16   combine the y terms, move the 7 to the other side
              -7y = 9    divide by -7
                y = -9/7

Now we have to figure out what x is when y is -9/7.  So let's plug -9/7 into
the second original equation (we could use either one, but the second one 
looks a little easier):

x - 2y = 8
x - 2(-9/7) = 8     solve for x
x = 38/7

So the answer is the ordered pair (38/7, -9/7).  You can plug that in for
x and y into both equations to check and see whether it's correct.

>Also how do I graph the line 2x-3y=6

Try using the same method: find four points on the line, then connect them.

>What is the slope of the line connecting the points (2,3) and (-2,4)

The formula for the slope between two points (x1, y1) and (x2, y2) is

                                  (y1 - y2)
                                  ---------
                                  (x1 - x2)

>What is the slope of the line 3x-5y=8                   (What do i do on this?)

For this, you can solve for y, so that you get an equation in the form
y = (something)*x + (something else).  In this equation (which is known as the
slope-intercept form of the equation for a line), the first "something" is the
slope of the line.  Most people write the general form of this equation
as y = mx + b.

>name 3 pts. which are on the graph of the line 3x+4y=12.

You can use the same method as in the very first problem: pick random values
for x, then see what y is.

-Doctor Ken,  The Geometry Forum
    
Associated Topics:
High School Basic Algebra

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