Two young mathematicians discuss the standard form of a line.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, I think we’ve been too explicit with each other. We should try to be more implicit.
Riley
I. Um. Don’t really…
Devyn
I mean when plotting things!
Riley
Okay, but I still have no idea what you are talking about.
Devyn
Remember when we first learned the equation of a line, and the “standard form” was or something, which is totally useless for graphing. Also a circle is or something, and here isn’t even a function of .
Riley
Ah, I’m starting to remember. We can write the same thing in two ways. For example, if you write then is explicity a function of but if you write then is implicitly a function of .
Devyn
What I’m trying to say is that we need to learn how to work with these “implicit” functions.
Consider the unit circle The point is on this circle. Reason geometrically to determine the slope of the line tangent to at .
Draw a picture.
The slope is .
Consider the unit circle The point is on this circle. Reason geometrically to determine the slope of the line tangent to at .
Draw a picture.
The slope is .