While slope is used to describe the measurement of steepness of a straight line, it can also be used to describe the cross-country ski slopes that Oscar likes to frequent.

Below is a break-down of the types of slopes that Oscar encounters on his cross-country graphing adventures.

Oscar

bullet Positive Slopes:

oscarup
Positive Slope

Lines that slant "up-hill" on the graph,
from left to right, have a positive slope.

Such "hills" require Oscar to increase his energy level to get up these hills.
He must add (+) energy
to get up the hill.

Graphed lines that go
"up-hill", from left to right, have positive slope.

 

bullet Negative Slopes:

Oscardown
Negative Slope

Lines that slant "downp-hill" on the graph,
from left to right, have a negative slope.

Such "hills" require that Oscar decrease his energy level in an attempt to slow down.
He must subtract (-) energy
to slow down.

Graphed lines that go
"down-hill", from left to right, have negative slope.

 

bullet Zero Slopes:

Oscarzero
Zero Slope

Lines that are horizontal
(straight across from left to right)
have zero slope.

Such "paths" do not go up-hill or down-hill. Oscar does not need to increase,
or decrease, his energy level.
The change in his energy level is zero.

Graphed lines that are horizontal have a
slope of zero.
Horizontal lines have lots of "run", but no "rise". Therefore, rise/run = 0/number = 0.

 

bullet No Slope (or Undefined Slope):

oscarhelp
No Slope
or Undefined Slope


Lines that are vertical (straight up and down) have no slope (or undefined slope). This means the slope does not exist.
It does not mean the slope is zero.

Oscar cannot ski on such "paths".
Broken bones await him at the bottom.

Graphed lines that are vertical have no slope
(or undefined slope).
Vertical lines have lots of "rise", but no "run". Therefore, rise/run = number/0 = undefined.

 


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