Question 66
We say that two real numbers $r$ and $s$ are *close* if $|r - s| = 10^u$ for some integer $u$. Let $y = ax + b$ be a linear function, for which there exist close numbers $x_1$ and $x_2$ so that the corresponding $y_1$ and $y_2$ are also close. Prove that for any close numbers $x'_1$ and $x'_2$, the corresponding $y'_1$ and $y'_2$ are also close.