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Graphing Linear Equations

Date: 04/11/2003 at 17:40:47
From: Aimee
Subject: Graphing linear equations and Inequalities

I was recently on math.com and I am a little confused. They asked me 
to find the slope and the y-intercept. But how do I find the points on 
the line so that I can get the answers? There aren't any dots on the 
lines to find the coordinates.

Please help.


Date: 04/14/2003 at 00:15:07
From: Doctor Ian
Subject: Re: Graphing linear equations and Inequalities

Hi Aimee,

You can choose _any_ points on the line to find the slope and 
intercept.  

For example, pick any value of x, and mark it on the x-axis.  


    +---|---*---|---|---|
        1   2   3   4   5 

Then move straight up (or down) until you hit the line.  

    |          /
  6 -         /
    |        /
  5 -       .
    |      /.
  4 -     / .
    |    /  .
  3 -   /   .
    |  /    .
  2 - /     .
    |/      .
  1 /       .
    |       .
    +---|---*---|---|---|
        1   2   3   4   5 

Then move straight over until you hit the y-axis.  

    |          /
  6 -         /
    |        /
  5 *........
    |      /.
  4 -     / .
    |    /  .
  3 -   /   .
    |  /    .
  2 - /     .
    |/      .
  1 /       .
    |       .
    +---|---*---|---|---|
        1   2   3   4   5 

Those x and y values are the coordinates of one point on the line.  In
this case, 

   x=2, y=5  -->  (2,5)  

is one point on the line.  Do the same thing again to find a second
point, 

    |          /
  6 -         /  
    |        /  
  5 *........   
    |      /.   
  4 -     / .   
    |    /  .   
  3 *....   .   
    |  /.   .   
  2 - / .   .   
    |/  .   .   
  1 /   .   .   
    |   .   .   
    +---*---*---|---|---|
        1   2   3   4   5 

and you can use those two points to find the slope. Note that you may
need to do a little exploring to find x values that give you nice,
round y values. That isn't strictly necessary, but it can make your
calculations easier.  

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Equations, Graphs, Translations
High School Linear Equations

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