



OK,
up to now this X Y graphing hasn't been too exciting 


or
too valuable, but here's the payoff. 





When
we have an equation with just X's and Y's, 


that
is, no exponents in the equation (like X
^{3} or anything) 


all
of the X = this and Y = that solutions to the equation 


will
be on a straight line on the graph! 





Once
we have 2 points, we just draw the line that goes between them 


to
get all of the possible X = this and Y = that 


solutions
to the problem. 





The
line (and the answers) go on in both directions forever. 


To
show this, we always draw arrow heads 


at
the ends of the lines. 





So
we can take the graph from the last page ... 











and
do this! 











Let's
do another one ... 





Example: 





X + 4 = Y






For
the first X point, chose X = 0. 


It's
usually the easiest one to do.






X + 4 = Y




(0) +
4 = Y 



4 = Y 






So
we have X = 0, Y = 4. 


Mark
it on the graph ... 











Did
you notice that whenever X = 0 


the
point is on the Y number line (Y axis)? 


Also
if Y = 0 for a point 


it
will be on the X axis. 





So
we need one more point. 


Let's
try X = 2 ... 


X + 4 = Y




(2) +
4 = Y 



2 = Y 






So
we have X = 2, Y = 2. 


Draw
in that point ... 











Now
with 2 points, we can draw in the line 


that
all the X = this and Y = that points are on ... 











In
the first example, the line was going up 


as
it went from left to right. 


In
this one, the line is going down 


as
it goes from left to right. 





It
sort of looks like the side of a hill 


OR
A SKI SLOPE. 





Math
people decided to call this "going up" 


and
"going down" thing the SLOPE of the line. 





WOW!
A name that makes sense! Amazing. 


The
names that other parts of the graph get 


are
harder to remember. 





The
number lines themselves are called AXIS. 


The
X number line is the X AXIS. 


The
Y number line is the Y AXIS. 


The
X and Y value pair numbers are called COORDINATES. 


The
point where the X and Y number lines cross 


is
called the ORIGIN. 











copyright 2005 Bruce Kirkpatrick 
