The points $A(5,-8), B(9,-30)$ and $C(n, n)$ are collinear (that is, lie on the same straight line). What is the value of $n$ ?
Since $A(5,-8), B(9,-30)$, and $C(n, n)$ lie on the same straight line, then the slopes of $A B$ and $A C$ are equal.

Thus,

$$
\begin{aligned}
\frac{(-30)-(-8)}{9-5} & =\frac{n-(-8)}{n-5} \\
\frac{-22}{4} & =\frac{n+8}{n-5} \\
-22 n+110 & =4 n+32 \\
78 & =26 n \\
n & =3
\end{aligned}
$$

Therefore, $n=3$.

ANSWER: 3