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in this video we will look at some special cases of slope if you recall slope is a measure of steepness of a line if we look at this first line on the left a horizontal line we can calculate slope by doing the rise over run however youll notice from 11.2 the next there is no rise this would be a rise of 0 over a run of 3 units 0 over 3 reduces to 0
we say this line has a slope of 0 zero slope looking at this picture it makes sense that we call this a zero slope because slope is a measure of steepness you could imagine a little man walking across this line would have no problem because of its absolute flatness because it is a simple walk across with no incline there is a zero slope it doesnt get any flatter than zero a measure of steepness
contrast this with the line on the right again slope is calculated as the rise over the run with the two points given we see we rise 5 units however there is no horizontal change there is no run if you recall we are not allowed to have 0 in the denominator of a fraction we say this is undefined this slope is undefined because it is so incredibly steep it has no slope which makes sense
if slope is a measure of steepness you could imagine a man trying to walk up this slope would have a pretty difficult time about it he would actually fall because it is so absolutely steep if this is the steepest possible line we need a number that represents the steepest possible value while a million is steep you could go as steep as a slope of a trillion or a googolplex we could keep going steeper
we use undefined to represent this largest possible number of an infinite slope of maximum steepness it is important to note that there is a difference between a zero slope which is completely flat and no slope which is completely horizontal it is often confused between one and the other zero slope is an easy walk in the park no slope is a cliff that youve fallen off of because its undefined in how steep it is
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