



Math
people wanted a really good way 


to
talk about how steep the graph line was. 





Let's
look at an equation that we worked with 


on
the last page ... 











The
way "the steepness" of the line is measured 


is
pretty simple ... 





STEP
1: 


Choose
any point on the line. 


Label
the X value of that point X_{1} 


Label
the Y value of that point Y_{1} 





So
let's choose the point (0, 3) for this. 


That
means X_{1} = 0 and Y_{1} = 3. 





STEP
2: 


Choose
any other point on the line. 


Label
the X value of that point X_{2} 


Label
the Y value of that point Y_{2} 





So
choose the point (2, 1) for this one. 


That
means X_{2} = 2 and Y_{2} = 1. 


(Hey,
it was the only other point we had worked out!) 





STEP
3: 


Take
the 4 values and put them into this formula ... 











and
find the answer ... 











So
the slope of the equation Y = 2X  3 is 2. 





Math
people sometimes call the slope of an equation "m" 


(who
knows why). 





So
we say that for the equation Y = 2X  3, that m = 2. 





The
slope actually tells us 


how
many units the line goes up (+) or down () 


for
each unit it goes from left to right. 





The
amount the line goes up 


is
how much bigger Y gets. 





The
amount the line moves to the right 


is
how much bigger X gets. 





Getting
bigger (or smaller) is a change. 


Another
little code that you may see 


in
math or science is a triangle "D" 


This
triangle has a name. 


It
is called delta. 





The
slope is the amount that Y changes, 


divided
by the amount that X changes. 


This
is sometimes written as ... 











Did
you notice in the equation that the number 


next
to X term was 2, and so was the slope? 





Did
you think that was just luck? 


NOPE! 





Whenever
the equation is set up like ... 





Y = (some
number)X + (some other number) 





The
number next to the X term (it's coefficient) 


is
the slope. 





Not
only that, the "(some other number)" is the Y value 


where
the equation line crosses the Y number line (axis). 





SO,
in the equation ... 











The
larger the slope number is, 


the
faster the line goes up from left to right ... 











We
say that the equation with the slope of 2 


is
STEEPER than the equation with the slope of 1. 





If
the number next to the X is negative, 


the
equation line goes down from left to right ... 











If
two equation lines have the same slope, 


they
have equation lines that are parallel 


or
are the same line ... 











But
if two equations don't have the same slope, 


their
equation lines MUST cross somewhere. 





copyright 2005 Bruce Kirkpatrick 
