For two functions
$$\begin{aligned}
& f ( x ) = \left\{ \begin{array} { c c }
x ^ { 2 } - 4 x + 6 & ( x < 2 ) \\
1 & ( x \geq 2 )
\end{array} , \right. \\
& g ( x ) = a x + 1
\end{aligned}$$
When the function $\frac { g ( x ) } { f ( x ) }$ is continuous on the entire set of real numbers, what is the value of the constant $a$? [4 points]\\
(1) $- \frac { 5 } { 4 }$\\
(2) $- 1$\\
(3) $- \frac { 3 } { 4 }$\\
(4) $- \frac { 1 } { 2 }$\\
(5) $- \frac { 1 } { 4 }$