Expert: Paul Klarreich - 8/15/2007

Question
My teacher is one of those give you one example very fast then let you loose to do it. Its very difficult for me to learn that way. I would be very much appreciative if you could explain forms to me. Like slope intercept, point slope intercept, and general. Thank you.

Answer
Hi, Anna,

A 'form' is a pattern that represents many examples.  Each of the examples is an 'instance' of the form.  

Typically, the 'form' has both variables and symbolic constants (sometimes called parameters) in it.  But each example has actual constants instead of the symbolic ones; it will have the variables.  It is simply up to you to know, for each form, which is which.  You are also supposed to learn what the parameters tell you -- the interpretation.  Of course, that is different for each form.

Example:  the 'slope-intercept' form.

The pattern:  y = mx + b.

The parameters:  m, b.
The variables:  x,y.

In any example, you WILL see the letters x,y; you will NOT see the letters m,b.  [OK, the letters x,y might be replaced by other letters, but not by constants.]

One instance:  y = -3x + 2, in which the parameters are  m = -3, b = 2.

Interpretation:  

1. This represents the equation of a straight line graph.    
2. m = -3 means the slope is -3 and the line will be tilted downward.
3. b = 2  means the line passes through the point (0,2)

I hope this helps.  I have been away on vacation for some time and didn't see this until today.