Algebra Period 4

SLOPE
: 7-4

First, let's talk about what the word "slope" means in the real world:


You can think of the slope of a line as the slope of a ski mountain -


When you're climbing up, it's positive


When you're sliding down, it's negative
 (if you're looking at the mountain from left to right)


The steeper the mountain, the higher the slope value


(A slope of 6 would be an expert slope because it
is much steeper than a slope of 2 which would be an intermediate's slope)


"Bunny slopes" for beginners will be lower numbers,
 generally fractional slopes (like 1/2 or 2/3)



A good benchmark to know is a slope of 1 or -1 is a 45 degree angle


You can also think of slope as rise/run - read this "rise over run"


Rise is how tall the mountain is (the y value)


Run is how wide the mountain is (the x value)


A 1000 foot high mountain (the rise) is very steep if it's only 200 feet wide (the run) (slope = 5)


Another mountain that is also 1000 feet high is not very steep if it is 2000 feet wide (slope = 1/2)


You can think of slope as a calculation using 2 coordinates.

We use m to denote slope:


m = rise/run

change in y
change in x

Rise = Change in y value = Difference in y value = y₂ - y₁
Run = Change in x value = Difference in x value = x₂ - x₁
THE LITTLE 1 AND 2 SUBSCRIPTS JUST STAND FOR Y VALUE OF THE FIRST POINT AND Y VALUE OF THE 2ND POINT.

To calculate slope you need 2 coordinates.

It doesn't matter which one you start with.

Just be consistent!

If you start with the y value of the FIRST point, make sure you start with the x value of the FIRST point!

If you start with the y value of the SECOND point, make sure you start with the x value of the SECOND point!



You can count the slope of a line:


1) Beginning with one point, count up to another point; however far that is, make that the numerator of your slope (because the y value of slope is the numerator)


2) Now count how far over the point is across - You'll need to either go right or left.


Make this the denominator of your slope (because the x value is the denominator of slope)


If you went to the RIGHT, the value is POSITIVE (x values going to the right or positive)


If you went to the LEFT, the value is NEGATIVE



Special slopes:


Horizontal lines in the form of y = have slopes of zero (they're flat!)


Vertical lines in the form of x = have no slope or undefined because the denominator is zero