Think of walking to the store. If the ground is flat, walkin' is eeeeasy.
If there is a little bit of a hill, it gets not so easy. If there is a
huge hill on the order of Mount Everest, I'm willing to bet you'd forego
that Pepsi and Doritos. What is it about hills that make them so darn hard
to climb? The answer is SLOPE. Slope is a measure of the rate of
change, whether it be change in speed, distance, bank balance, number of
rabbits in a forest or number of pimples on your face. The larger the slope,
the faster the rate of increase or decrease. To find the slope of a line,
you need to know two things-two coordinates on the line. Slope is the ratio
of the change in the y-value {the rise} to the change in the x-value{ the
run}. Slope has been known to go by the infamous alias "m". Once you have
identified your two points in a police lineup, you are ready to go. First
you grab one set of coordinates and throw the label on them of (X1, Y1).
All it means is this is the first point you laid eyes on. Then by process
of elimination, the other point is called (X2, Y2).
[Drum roll] Dum-ta-da-dum! The formula, please...
slope (aka m) = Y2 - Y1
X2- X1
Say for example, you discovered that your two points were (1, 4) and (3, 50)
Your slope would be m = (50-4) = 46 = 23
(3-1) 2
Slope can take on many identities- it can be positive, negative, big
or small. Fractions, decimals and whole numbers oh my!
Positive slopes are very optimistic-they are always increasing.
Negative slopes are much more cautious-they are always looking to decrease
their value. Slope can even be ZERO- this means totally absolutely flat
line, no change in the patient's condition. There is also a slope
so big and ugly and mean that we call it undefined-this is a line that
goes straight up and down like the wall of an impenetrable fortress. You
will find this slope when you input values into your calculator and get
the big E on your screen-this means you have tried to force your calculator
to commit the illegal act of dividing by zero and it has refused to oblige.
So to recap:
Positive slope: an increase in your CD collection
Negative slope: a decrease in your cash flow as a result of an increase
in your CD collection.
Flat slope-no change in either, they didn't have what you wanted at
Music World
Undefined slope-when you try to increase your CD collection WITHOUT
decreasing your cash flow; when caught, the mall doors are a barrier that
you cannot surmount.
Y-intercept
Oddly enough, this term actually means what it says. This is the place where your line crosses or "intercepts" the y-axis. The y-intercept represents a starting point. Some things don't start from zero, like starting out from a friend's house to go to the mall instead of starting from your house. It can also represent when you start skiing downhill- you didn't start from the bottom; the chair lift had to take you to the top first.The y-intercept also goes by the pseudonym "b". Why b and not y? Well, y was already taken for the name of the axis, "i" was already in use for interest, and poor little b was standing alone and unemployed. So they claimed it in the name of y-intercept and it has been so ever since. For much the same reason as above, slope could not be represented as s because s was already pulling double duty as speed and seconds and refused to take on a third job.
Once you got this thing, whaddya do with it?
You take the general equation of a line, y = mx + b MEMORIZE this formula, you will need to know it for the rest of your unnatural mathematical lives.
(Ed. note: a lot of people cry out in fear when they notice that their line comes nowhere near the y-axis. I say now and tell you again, get out your trusty ruler and by gosh, make that line meet the y-axis. If you really can't make it so, seek professional help -you either have a very odd line or are having trouble with the term RULER)
Now suppose you manage to notice that the line from the slope equation
above happens to cross the y-axis at 2. Take your number from above,
m = 23 and your number now, b =2 and plug em in to the general, immutable,
unchangeable y = mx + b ;
which gives you y = 23X + 2 , which is a wholly respectable
equation and voila, there ya go,. you got your equation of the line.