



So
what we're going to do 


is
draw a picture of the equation. 





Maybe
you've seen something called a number line. 


It
looks like this ... 











In
these equations, we have two letters: X and Y 


To
see them both at the same time, 


we're
going to use two number lines. 





One
that looks like this to record the X values ... 











and
one that looks like this to record the Y values ... 











We're
going to use them both together at the same time. 


Like
this ... 











Now
here's the trick. 


When
we used a single number line 


we
put the dots right on the line. 


When
we use an X and a Y number line together, 


we
usually don't put the dots right on the lines. 


Here's
what we do ...






Let's
say we have an equation like ... 





2X  3 = Y 





and
we chose X = 2 for our first X value. 


Why
did I choose 2? Because I like 2. 


When
YOU do these problems by yourself



then
you can chose any number that you like! 





2(2) 
3 = Y 



4  3
= Y 



1 = Y 






So
we have X = 2 and Y = 1. 


To
find that point go to X = 2 on the horizontal number line. 


And
draw a line up and down (vertically) 


and
go to Y = 1 on the vertical number line 


and
draw a line from left to right (horizontally). 


Where
they cross, is the point where X = 2 and Y = 1. 











We
draw a dot at that point 


and
sometimes even write down the X and Y values next to it. 


If
we have a lot of points to draw, 


it
might take up too much space to write 


X
= 2 and Y = 1 or something like that at each point. 


So
instead, we just write (2,1). 


The
X value is always listed first. 





So
we have ... 








Let's
find another point. 


How
about when X = 0 ... 





2(0) 
3 = Y 



0  3
= Y 



3 = Y 






So
where X = 0, Y = 3 


Find
that point on the drawing ... 











So
since X = 0, one of our lines is on the Y number line 


(called
the Y axis). 


The
point is at Y = 3 on the Y axis. 


The
point gets named (0,3) ... 











Showing
both points together at the same time we have ... 











copyright 2005 Bruce Kirkpatrick 
