I2.1 If $A(1,3), B(5,8)$ and $C(29, a)$ are collinear, find the value of $a$.
The slopes are equal: $\frac{8-3}{5-1}=\frac{a-8}{29-5}$
$$
\begin{array}{l}
\frac{a-8}{24}=\frac{5}{4} \\
\Rightarrow a-8=30 \\
a=38
\end{array}
$$