What is the Rule of Correspondence in Mathematics?

[sfeld]

A = {(x,7)}: (1,2), (2,5), (3,8), . . .} Answer: y = 3x - 1

Can someone explain the rules of correspondence. I read it in the book that I have several times, but it doesn't explain it fully 100%.

 

[Galileo]

Rules of correspondence??
..uhm.. I don't know what you mean, or what that your notation is about.
But if you are looking for the equation of a line through the points (1,2), (2,5) and (3,8), two points will suffice.

Going 1 unit in the x direction gives an increase of 3 in the y direction. that determines the slope. Try it from there.

If you mean something else. Just ignore me.

 

[HallsofIvy]

It's not quite clear what what you are asking. Given something like
{(x,y): (1,2), (2,5), (3,8), . . .} (you had {(x,7)} but you MEANT that), there is no way to determine a single rule- there exist an infinite number of rules that give those pairs but differ on others. It is possible to ask "what is the simplest rule". I recently gave a rather complicated answer to that question in a different thread.
In any case, I suspect what you want is the other way around: How do check to see IF y= 3x-1 is correct., The answer is, calculate it and see happens:
if x= 1, y= 3(1)-1= 3-1= 2=> (1,2) checks
if x= 2, y= 3(2)-1= 6-1= 5=> (2,5) checks
if x= 3, y= 3(3)-1= 9-1= 8=> (3,8) checks

Since we have only 3 points, that's all we can do.