Linear Equations with Only X or Y instead of Both

Date: 04/09/2008 at 18:12:26
From: Jenny
Subject: Linear Equations Without and X value or Y value

Dr. Math,

My math teacher didn't explain what to do if the linear equation 
only has one variable (X or Y) instead of both.  We're supposed to 
find X in terms of Y.
 
Ex: y + 2 = 0
Ex: 2x - 1 = 0

What are you supposed to do if you only have a X, or just a Y?  How 
do you know if a linear equation is zero slope or unidentified?  How
are you supposed to graph a line that's zero or unidentified?  Also, I
have no idea of how to graph the line with only one point.  Do you
just create a straight line?


Thanks!

Jenny

Date: 04/10/2008 at 09:06:38
From: Doctor Ian
Subject: Re: Linear Equations Without and X value or Y value


Hi Jenny,

You can always use a coefficient of 0 for the "missing" variable.  So 

  y + 2 = 0

becomes

  1y + 0x + 2 = 0

What does this tell us?  It means that the value of y doesn't depend
on the value of x.  That's sort of the description of a horizontal
line, isn't it?  And in fact, if we try to solve for y, we get

   y = -0x - 2

which means the slope is zero... which is also one way to define a
horizontal line. 

With the other example, 

   2x - 1 = 0
   
we can use the same idea to get

   0y + 2x - 1 = 0

Looking at this, we see that the value of x doesn't depend on the
value of y.  That's the description of a vertical line, isn't it?  And
if we try to get the slope-intercept form, we get

    y = (-2/0)x + 1/0

and the slope is undefined.  Which is another way to define a vertical
line.  Does that make sense?

You wrote:

>Also, I have no idea of how to graph the line with only one point. Do
>you just create a straight line?

You can use those equations to get more than one point.  For example, 

   0y + 2x - 1 = 0

is true when x is 1/2 and y is 0, right?  So (1/2,0) is one point on
the line.  It's also true when x is 1/2 and y is 1.  So (1/2,1) is
another point.  

In fact, if you just solve it for x, you get

   x = 1/2

which tells you that (1/2,anything at all) is a point on the line. 

So pick two of them, and fill in the graph as usual.

Does this help? 

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

Date: 04/10/2008 at 18:11:55
From: Jenny
Subject: Thank you (Linear Equations Without and X value or Y value)

THANKS!!!!!!!!=)