Lines and t-tables

Date: 11/09/96 at 16:06:36
From: Emilee Anderson
Subject: graphs

-2x-4y=   I have to do a t-table and I just don't get it at all!                                                                                                       

Date: 01/27/97 at 10:19:16
From: Doctor Jimbo
Subject: Re: graphs

Emilee,

People use t-tables to get an idea of what a graph looks like. 
Unfortunately, the equation you have submitted is missing a righthand 
side, so it's not an equation.  (It's kind of like a sentence without 
a verb - it just doesn't make sense as it is.)

I'll try changing your equation a bit, so that it makes sense.  
How about we try -2x-4y=3 instead?

To use a t-table with this sort of an equation, some people make a 
list of one of the two variables and then figure out what the value 
of the other variable must be.  For instance, we can make a table of 
x-values, and find out what y has to be for each of them.

I'll try this table:

  x | y
 -------
  0 | 
  1 |
  2 |
  3 |

Now, the task is to figure out what numbers have to go in the 
righthand side.  Let's start with the first value for x, x=0.  
Now you ask yourself, "If x is 0, what does y have to be?"

Plug in 0 for x, and our equation becomes:

      -2x-4y=3        (the original equation)
 -2(0) - 4y = 3       (since x = 0)
     0 - 4y = 3       (-2*0 = 0)
          y = 3/(-4)  (divide both sides by -4)
          y = -3/4    (simplify)

Now I can put -3/4 in for y on the first line of my table.  This means 
that based on our equation, if x is 0 then y has to be -3/4.  
Continuing on, I could use x = 1 from the next line, and find that

 -2(1) - 4y = 3      (x = 1)
    -2 - 4y = 3      (simplify)
        -4y = 5      (add 2 to both sides)
          y = -5/4   (divide by (-4) and simplify)

When I'm done, my table will now look like this (I've left some for 
you to check):

  x |   y
 ---------
  0 | -3/4
  1 | -5/4
  2 | -7/4
  3 | -9/4

To create a graph, you plot those points: 

  (0,-3/4), (1,-5/4), (2,-7/4) and (3,-9/4).  

You should be able to connect them with a straight line.

You may wonder how I chose the values for x.  It doesn't really 
matter much.  Just make sure you use a few, and that they're close 
enough to fit on a graph, but far enough apart to show you what's 
going on.

One important thing about t-tables is that they work well with 
straight lines and fairly simple graphs.  When you start working with 
really complicated equations, though, you have to be careful because 
t-tables don't always show you everything that's going on.

Good luck.

-Doctor Jimbo,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/