The Vertical Line Test can be used to determine if a relation is a function as follows. Check if any vertical line ever crosses the relation more than once. If it does, the relation has failed the vertical line test and is not a function. About half of calculus is concerned with finding the slope of any function anywhere. Slope is thus an important concept but should already be familiar.
Perpendicular lines have slopes which are negative reciprocals.
This should be well studied in Algebra, so only a quick review is presented in today's activity. It is important to understand the difference between positive , negative , zero , and undefined slopes , and that is also covered in today's activity. If the slope is negative, y decreases as x increase and the function runs downhill. Vertical lines are problematic in that there is no change in x . Thus our formula is undefined due to division by zero.