



So
now we can graph equations like ... 





Y = 3X  4






without
much problem. 





The
graph of this line has a slope of 3 (the X coefficient). 


We
can also see pretty easily that when X = 0, Y = 4. 


With
a bit more work, we can also see that 


when
X = 1, Y = 1 ... 






Y = 3X
 4 



Y =
3(1)  4 



Y = 3 
4 



Y =  1 





So
we can graph this puppy ... 











This
wasn't too bad, but when some people see an equation 


that's
only slightly different , they lose it completely. 


Say
something like ... 





Y > 3X  4 





This
thing is no big deal. 





Here's
what you do with it. 





STEP
1: 


Pretend
it's got an equal sign and graph it.






STEP
2 


Now,
pick some test point on the graph that's not on the line. 


and
see if it makes the inequality true. 


(X
= 0, Y = 0 is a good one if it's not on the line) 






Y >
3X  4 



0 >
3(0)  4 



0 >
 4 which is
true! 





If
the inequality is true when we put in the test point, 


then
everything on the same side of the graph line 


as
the test point gets shaded. 





If
the inequality is NOT true when we put in the test point, 


then
everything on the OTHER SIDE of the graph line 


from
the test point gets shaded. 











STEP
3: 


The
last thing to deal with is the line itself. 


If
the equation uses ³
or £ then
the line is solid 


If
it uses > or
<
then the line is dotted. 





The
solid lines mean that the points on the line 


are
included in the area that makes the equation true. 





The
dotted line means that all of the points 


UP
TO the points on the line on the shaded side 


make
the equation true. 





Y
> 3X  4 uses >






so
the line is dotted ... 











Let's
try another one ... 





Example: 


Y
< X






STEP
1: 


Pretend
it's got an equal sign and graph it.






OK,
the slope = 1. When X = 0, Y = 0. When X = 2, Y = 2 ... 











STEP
2 


Now,
pick some test point on the graph that's not on the line. 


and
see if it makes the inequality true. 





OK,
we can't use (0,0) because it's on the line 


So
let's try the point where X = 2 and Y = 3. 












Y <
X 



3 <
2 nope, that's not true! 





That
means the side we shade 


is
the side that the point is NOT on ... 











STEP
3: 


The
last thing to deal with is the line itself. 


If
the equation uses ³
or £ then
the line is solid 


If
it uses > or
<
then the line is dotted. 





The
equation uses the less than symbol, 


so
the equation has a dotted line ... 











copyright 2005 Bruce Kirkpatrick 
