Graphing Linear Equations

Date: 12/26/2001 at 23:26:31
From: Cindi Smith
Subject: Slope-intercept: Graphing linear eqations

Give the intercepts of 7x - 2y = 2.

I recall doing something like this before but I do not want to steer 
my son wrong. Please help with this problem - maybe it will jar my 
memory and I will be able to help him with his studies.

Thank you for your help.

Date: 12/28/2001 at 18:45:47
From: Doctor Tim
Subject: Re: Slope-intercept: Graphing linear eqations

Thanks for writing, Cindi.

The intercepts are where the graph crosses the x and y axes. And that 
happens where x = 0 (for the y axis) and y = 0 (for the x axis). If 
this seems backward, think about it until it comes clear.

For an equation in the form you have, you find the x intercept by 
setting y = 0:

   7x - 2(0) = 2
          7x = 2
           x = 2/7

And similarly for the y-intercept.

Don't forget that you can always check by plugging in. If you put 
(x = 2/7, y = 0) into the equation, does it balance? Yes. That means 
that that point - (2/7,0) - is on the line.

Note: "slope-intercept" form is where you solve for y first. In this 
case, to get y alone on one side,

   7x - 2y = 2
     add 7x to both sides
       -2y = 2 - 7x
     divide both sides by (-2)
         y = (7/2)x - 1

There, (7/2) is the slope, and -1 is the intercept (it's the 
y-intercept in this form). Most books write this 

   y = mx+b
       Some write
   y = ax + b
       and some (especially statistics books) write
   y = a + bx

but they all mean the same.

- Doctor Tim, The Math Forum
  http://mathforum.org/dr.math/