Linear Regression Ttest

Hi, I just have a general question.
What are the conditions and assumptions (or rules of thumb, or whatever you refer to them as) for a Linear Regression t-test. I only have three (1. SRS, 2. for any value of x the y values form a normal regression, 3. The response has a straight line relationship) and I am under the impression that there are more. Also, I'm not sure how to prove that number 2 is true.
Thanks,
Kathy

I did some more research and I found, the last condition "For each given value of x the standard deviation of y is the same." How does one determine this?
I also haven't been able to find the proper way to test condition 2 "for any value of x the y values form a normal regression." Do you just look at it? Graph the y points for each x? What if their arn't enough points to determine a pattern? Would you just assume that it would be true, if there was more data?
Thanks,
Kathy