# What is the reason for using a “Lines-Oracle” in the PCP Theorem?

I'm trying to understand the proof of the PCP Theorem in "Complexity and Approximation" by G. Ausiello et al. and came across the low degree test which is used to check if a function $f$ given as oracle (or "auxiliary proof") is close to some degree $d$ polynomial. The test uses another "Lines-Oracle" for retrieving $d+1$ coefficients for univariate polynomials defined on lines. Then the test simply compares the univariate polynomial with respect to a random line on a random point with $f$. Why is this "Lines-Oracle" necessary? I mean one could just interpolate $f$ on a random line (with the same amount of queries) and do the same check. Is this just for convenience?

The lines oracle is used to decrease the query complexity of the test from $d+1$ to $2$, at the expense of using a larger alphabet.
If you don't mind making $d+1$ queries, then the lines oracle is indeed unnecessary. However, it is usually better to make two queries over a large alphabet than $d+1$ queries over a small alphabet.
A second reason, which is very related to the first one, is that many hardness-of-approximation results are proved based on $2$-query PCPs, but can not be proved using based on a PCP with more queries.